### Angles and Parallel Lines

- Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent
- Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent
- Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary
- Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent
- Perpendicular Transversal Theorem: In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other

### Angles and Parallel Lines

The lines seperating lanes on the road.

- Parallel.
- State the postulate or theorem that allows you to conclude that ∠1 ≅∠2.

m||n, p||q, m∠1 = 125

^{o}, find m∠2, m∠3, m∠4 and m∠5.

- m∠2 = m∠1 = 125
^{o} - m∠3 + m∠2 = 180
^{o} - m∠3 = 180
^{o}− 125^{o}= 55^{o} - m∠5 + m∠2 = 180
^{o} - m∠5 = 180
^{o}− m∠2 = 180^{o}− 125^{o}= 65^{o}

^{o}.

m||n, p||q, m1 = 70

^{o}, m∠2 = x + 4, m∠3 = 2y + 4, m∠4 = 5z + 5, find x, y and z.

- 2∠ ≡ ∠1
- m∠2 = m∠1
- x + 4 = 70
- x = 66
- ∠3 ≡ ∠2
- m∠3 = m2
- 2y + 4 = 70
- y = 33
- ∠4 ≡ ∠1
- m∠4 = m∠1
- 5z + 5 = 70

.

The lines seperating lanes on the road.

.

.

If m||n and p⊥m, then p⊥n is ______ true.

^{o}, m∠3 = 70

^{o}, find m∠2.

- ∠1 ≡ ∠4
- m∠1 = m4 = 60
^{o} - m∠1 + m∠2 + m∠3 = 180
^{o}

^{o}− 60

^{o}− 70

^{o}= 50

^{o}

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Angles and Parallel Lines

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Corresponding Angles Postulate
- Alternate Interior Angles Theorem
- Consecutive Interior Angles Theorem
- Alternate Exterior Angles Theorem
- Parallel Lines Cut by a Transversal
- Perpendicular Transversal Theorem
- Extra Example 1: State the Postulate or Theorem
- Extra Example 2: Find the Measure of the Numbered Angle
- Extra Example 3: Find the Measure of Each Angle
- Extra Example 4: Find the Values of x, y, and z

- Intro 0:00
- Corresponding Angles Postulate 0:05
- Corresponding Angles Postulate
- Alternate Interior Angles Theorem 3:05
- Alternate Interior Angles Theorem
- Consecutive Interior Angles Theorem 5:16
- Consecutive Interior Angles Theorem
- Alternate Exterior Angles Theorem 6:42
- Alternate Exterior Angles Theorem
- Parallel Lines Cut by a Transversal 7:18
- Example: Parallel Lines Cut by a Transversal
- Perpendicular Transversal Theorem 14:54
- Perpendicular Transversal Theorem
- Extra Example 1: State the Postulate or Theorem 16:37
- Extra Example 2: Find the Measure of the Numbered Angle 18:53
- Extra Example 3: Find the Measure of Each Angle 25:13
- Extra Example 4: Find the Values of x, y, and z 36:26

### Geometry Online Course

### Transcription: Angles and Parallel Lines

*Welcome back to Educator.com.*0000

*The next lesson is on angles and parallel lines.*0002

*OK, last lesson, we learned about the different special angle relationships, when we have a transversal.*0007

*The transversal with the other lines forms angles, and those pairs of angles have special relationships.*0017

*And one of them was the corresponding angles.*0030

*Now, the two lines that the transversal cuts through--remember: I said that the lines can be parallel, but they don't have to be.*0040

*So, even if the lines are not parallel, you are still going to have corresponding angles.*0050

*But then, now the postulate is saying that, if the lines are parallel, then the corresponding angles are congruent.*0056

*If these lines are parallel (let's say that they are parallel lines), then each pair of corresponding angles is congruent--only if the lines are parallel.*0068

*If we don't have parallel lines--if I have lines like this and like this--they are not parallel;*0083

*they don't look parallel, but I have a transversal--let's say 1 and 2: these angles are corresponding angles, but they are not congruent.*0093

*They are not congruent, but they are still corresponding; angles 1 and 2 are corresponding angles, but they are not congruent.*0105

*They are just called corresponding angles; so be very careful--only if the lines are parallel, then you can see that corresponding angles are congruent.*0112

*They are the same; they have the same measure; they are congruent.*0123

*Since these lines are parallel, I can say that angles 1 and 2 are congruent.*0127

*So, angle 1 is congruent to angle 2; and it goes with all of the pairs of corresponding angles,*0137

*like this one and this one--they are congruent...this one and this one, and this one and this one.*0145

*Each of the pairs of corresponding angles is congruent only if the lines are parallel--that is very, very important.*0152

*And that is a postulate; a postulate, remember, is any statement (such as this) that we can assume to be true.*0159

*It doesn't have to be proved; if it is a theorem (the next few are actually going to be theorems),*0170

* then they have to be proved in order for you to be able to use them, because it is not true until it is proven.*0176

*The next one: here is a theorem; now, we are not going to prove these theorems now, but they are shown in your textbooks.*0186

*The alternate interior angles theorem--just so you know, some kind of proof has to be shown for the theorems*0198

*in order for them to be counted as true and correct, and then, that is when we can use them.*0208

*But for now, since they are proven in your book, we are just going to go ahead and use them.*0214

*The alternate interior angles theorem says that, if two parallel lines are cut by a transversal*0219

*(meaning, if the two lines that are cut by a transversal are parallel), then each pair of alternate interior angles is congruent.*0225

*Again, from the last lesson: if I have two lines...now, I know I am repeating myself a lot,*0238

*but that is so that you will understand this, because I have seen a lot of students make careless mistakes with these,*0245

*always thinking that these are congruent; in this case, if I tell you that these lines are not parallel,*0258

*or if I don't even say anything about them being parallel, then you don't assume that they are parallel.*0265

*We just have to assume that they are not parallel; then we can't say that angle 1 and angle 2 are congruent.*0272

*We can say that they are alternate interior angles; that is the relationship; but they are not congruent in this case.*0277

*So, for lines being parallel (now I am telling you that the lines are parallel), then alternate interior angles*0286

*(let's say that this is angle 1 and angle 2)...angle 1 is congruent to angle 2.*0296

*If the lines that are cut by a transversal are parallel, then alternate interior angles are congruent; and that is the theorem, the other one.*0306

*The next one is the consecutive interior angles theorem: If two lines that are cut by a transversal are parallel,*0317

*then (this is the tricky part--not tricky, but this is the part that students really make mistakes on) the consecutive interior angles*0331

*are not congruent; they are supplementary--this is very important.*0344

*Consecutive interior angles, we know, are angles that are on the same side, like these two angles right here.*0351

*And they are both on the inside, the interior.*0357

*So, angles 1 and 2 are consecutive interior angles; but then, they are not congruent--they are supplementary.*0362

*Only if the lines are parallel, then consecutive interior angles are supplementary.*0369

*See how the other ones that we just went over are congruent: these are not congruent--they are supplementary.*0375

*You have to say that the measure of angle 1, plus the measure of angle 2, equals (supplementary means) 180.*0383

*That means that this angle measure, plus this angle measure, equals 180--very important.*0391

*And the next one: Alternate exterior angles, if the lines are parallel, are congruent.*0404

*So, here is a pair of alternate exterior angles; angle 1 is congruent to angle 2.*0415

*And that also works for this pair of alternate exterior angles, like 3 and 4; those will be congruent, also.*0425

*Here we have parallel lines that are cut by a transversal.*0442

*If AB (let's say that this is A, and here is point B--and these are the points, not the angles;*0445

*here is point C and point D...then AB is a line, so it is line AB) is parallel to line CD,*0460

*and line CA is parallel to line DB (and then I am going to add these parallel markers;*0471

*that means that these two are parallel lines, and then for these--this is another pair of parallel lines,*0484

*so that means that I have to draw two of them for these, because it is another pair), find the values of x and y.*0488

*So then, here we have 80; and then I need to take a look at x.*0500

*If I look for a relationship between this one and another one, even though these two have a relationship,*0508

*this has a variable x, and this has a variable z.*0517

*I would rather use this relationship, 4x and 80, because, if I am going to compare them, at least this one doesn't have another variable.*0521

*So, it is easier to solve; so then, if I look at these two, I am only dealing with this line, line AB, line CD, and line BD.*0530

*That means that line AC, I am going to ignore, because it is not involved in this pair of relationships.*0543

*Remember from the last lesson: you look at the pair, and when you have the special pair, it only has three lines involved.*0549

*It only has line AB, line CD, and line BD involved; the other lines that are there--cover them up.*0560

*Those lines are there for another pair of relationships, so just cover it up.*0567

*You don't need this line for this pair, so just ignore it.*0573

*And then, to solve it, the theorem (and the relationship between these two: they are alternate interior angles,*0583

*because BD would be the transversal between these two lines) says that if the two lines*0596

*cut by a transversal are parallel (which they are--we know that because it gives us that in here),*0604

*if the lines are parallel, then alternate interior angles are congruent.*0611

*Since the lines are parallel, I can say that these two angles are congruent.*0618

*Then, they are congruent, so 4x = 80; and I divide by 4: x = 20.*0621

*There is my x-value; and then, for my y, let's look at this one.*0638

*Well, with this one, I know that, since I have an 80 here, 80 is also congruent to this angle right here,*0651

*because they are corresponding, and I know that these two lines are parallel.*0667

*If these two lines are parallel, here is my transversal; that means that this angle right here and this angle right here are corresponding.*0670

*And as long as the two lines that are cut by the transversal are parallel, then corresponding angles are congruent.*0680

*So then, I can just write an 80 in here; and then, between this and this, they are vertical.*0685

*Now, I could have just done this angle right here to this right here; so there are many ways to look at it.*0694

*You can look at corresponding angles; if you didn't really see the alternate exterior angles--*0700

*if that is kind of hard for you to see--then you can just say that, OK, they are corresponding, and then these two are vertical.*0707

*And vertical angles, remember, are always congruent.*0711

*So, you can say that these two are the same, because they are vertical.*0717

*Or you can say that this and this are the same, because they are alternate exterior angles.*0722

*And those are the same, as long as the two lines are parallel.*0727

*So, either way: 4y + 10 = 80; then 4y = 70; so y = 35/2.*0730

*And that is just 70/4, and then you just simplify it to 35/2.*0755

*Now, it doesn't ask for the value of z, but let's just go ahead and solve it.*0765

*We know that 6z and 80 have a relationship.*0774

*Now, I know that this is 80, because we found x; x is 20; and 4 times x is 80;*0783

*and also because they are alternate interior angles, so whatever this is, this has to have the same measure.*0790

*So, either way we look at it: we can look at it as 6z with this one right here,*0798

*or we can look at this one with this one right here--same relationship, same value,*0801

*which also means that this one is also the same as 4x; this angle and this angle have the same measure.*0806

*Either way, the 6z with this angle right here are consecutive interior angles, or same-side interior angles.*0814

*Now, if the lines are parallel (which they are), then consecutive interior angles are supplementary--not congruent, but supplementary,*0826

*which means that I can't make them equal to each other.*0839

*Consecutive interior angles are the only ones that are not congruent from the special pairs of angles.*0844

*Supplementary--that means that I have to make 6z + 80 equal to 180.*0851

*6z = 100; z = 100/6, and then I can just simplify this to 50/3, and that is it; that is z.*0859

*OK, the last theorem from this section in this lesson is the perpendicular transversal theorem.*0897

*Perpendicular, we know, are two lines that intersect to form a right angle.*0904

*So, if I have a line like this and a line like this, and they form a right angle, then they are perpendicular.*0911

*But then, here we have a transversal involved; so in a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other.*0918

*Here are my parallel lines; I am going to show it by doing that.*0932

*If my transversal, which is this line right here, is perpendicular to just one of the lines*0936

*(it doesn't matter which one), as long as these lines are parallel (they have to be parallel),*0943

*if it is perpendicular to one of the lines, then it has to be perpendicular to the other line.*0951

*If this is perpendicular to this line, then it is going to be perpendicular to this line, as well.*0960

*And that is the perpendicular transversal theorem.*0967

*Now, if the two lines are not parallel (let's say like this), and then I tell you that this line is perpendicular to this line,*0969

*it is not going to be perpendicular to this line, because these lines are not parallel.*0983

*In this case, don't assume that it is perpendicular to both--that is only if the lines are parallel.*0990

*Let's do a few examples: State the postulate or theorem that allows you conclude that angle 1 is congruent to angle 2.*0999

*Now, remember: the only postulate was the corresponding angles one: that is the one where you have the angles in the same corner,*1007

*in the same position, in the same corner of the intersection--that is the corresponding angles postulate.*1015

*Everything else--the consecutive interior angles theorem, the alternate interior angles theorem,*1026

*the alternate exterior angles theorem--those are all theorems; so the only one is the corresponding angles postulate.*1034

*Here, what postulate or theorem allows you to conclude that angle 1 is congruent to angle 2?*1043

*We know that this is our transversal line, because it is the one that cuts through two or more lines.*1051

*Then, angle 1 and angle 2 are alternate exterior angles.*1056

*Now, if these two lines are parallel, then we can conclude that angle 1 is congruent to angle 2; let me show that these two lines are parallel, too.*1063

*Then, this would be the alternate exterior angles theorem.*1073

*And this one right here--we know that these are corresponding angles.*1097

*And the only way that the postulate will make them congruent (the only way we can apply the postulate) is if these two lines are parallel, which they are.*1106

*So, I can say that, by the corresponding angles postulate, angle 1 is congruent to angle 2.*1114

*All right, the next one: In the figure, line e is parallel to line f.*1134

*So, let me show this; it doesn't matter which way--I can just do like this, or I can just do like that.*1142

*AB is parallel to CD, so this one is parallel to this; and the measure of angle 1 is 73.*1149

*I am going to write that in blue; so this is 73, right here.*1158

*Find the measure of the numbered angles.*1165

*All of the numbered angles is what it is asking for.*1169

*Let's look at this: to look for the measure of angle 2, I know that angle 1 and angle 2 are supplementary, because they are a linear pair.*1175

*They form a line, and a line is 180 degrees.*1190

*So, all linear pairs are supplementary; so since linear pairs are supplementary, and these are a linear pair,*1196

*I can say that 73 plus the measure of angle 2 equals 180.*1208

*And then, to find the measure of angle 2, I have to subtract the 73; so the measure of angle 2 equals 107.*1218

*And then, the next one: the measure of angle 3--well, if you look at this, we know that these two lines are parallel.*1235

*This line intersects both of the parallel lines; so this is a transversal--this line segment AB is a transversal,*1246

*which means that angle 2 and angle 3 are alternate interior angles.*1256

*And by the alternate interior angles theorem, since the lines are parallel, we know that these angles are congruent.*1263

*Since the measure of angle 2 is 107, I can say that the measure of angle 3 is 107.*1272

*And then, the measure of angle 4: it is also alternate interior angles with angle 1, so by that theorem, again,*1284

*since the two lines are parallel, those two will be the same; so it is 73.*1303

*Then, the measure of angle 5 is corresponding with angle 5; angle 5 and angle 1 are corresponding,*1314

*because it is as if I extend this line segment, just to help me out here: these two lines are parallel;*1324

*here is my transversal; can you see that?--this is a line, and this is a line; here is that transversal;*1332

*angle 1 and angle 5 are corresponding, so if this is 73, then the measure of angle 5 has to be 73.*1344

*And then, the measure of angle 6--you can say that angle 6 is also corresponding with angle 3.*1354

*So, if you extend this out again, there is my intersection, angle 3, and then my intersection, angle 6.*1368

*The measure of angle 3 is 107, so the measure of angle 6 is also 107.*1378

*Angle 7 is alternate interior angles with angle 6, so that has to be the same, since the lines are parallel.*1386

*And the two lines involved would be this line and this line--can you see that?--this line and this line, and here is my transversal.*1399

*These two lines are parallel, so angle 6 and angle 7 are congruent by the alternate interior angles theorem.*1408

*And then, the last one, the measure of angle 8: it is supplementary with angle 6, because it is a linear pair.*1421

*Or it is alternate interior angles with angle 5, or it is corresponding with angle 4; there are a lot of different relationships going on here.*1431

*If you want to use the alternate interior angles theorem with angle 5 and angle 8, then it is going to be 73.*1447

*If you want to look at the corresponding angles postulate with angle 4, then it is also 73.*1457

*If you want to say that it is supplementary with angle 6 (it is a supplement to angle 6), then it is 180 - 107, which is 73.*1463

*You can look at it in many different ways.*1475

*That is it: see how all of the angle measures are either 73 or 107.*1482

*Since all of these lines are parallel--these pairs are parallel, and those two pairs of lines are parallel--*1488

*they are going to have only two different numbers, because all of their relationships are congruent or supplementary.*1498

*So, it is either going to be congruent, or it is just going to be a supplement to it.*1507

*Another example: BC is parallel to DE (that is already shown); the measure of angle 1 is 61 (this is 61);*1514

*the measure of angle 2 is 43; and the measure of angle 3 is 35.*1527

*This one is going to be a little bit more difficult, because we have lines that are closing in on the sides.*1539

*And sometimes it is going to be a little confusing, or a little bit hard to see the lines that you need to see.*1549

*And you are going to have to ignore these.*1561

*So, look at angle...let's see...3 and angle 4; if you look at BE as a transversal, and these two*1564

*as the lines that the transversal is intersecting, 3 and 4 are alternate interior angles.*1584

*But these two lines are not parallel--those two lines that the transversal is intersecting are not parallel.*1594

*So, you can't assume that they are congruent; you can't say that they are congruent, because look: the two lines are intersecting.*1602

*Even though they are alternate interior angles, you can't apply the theorem saying that they are congruent, because the lines are not parallel.*1612

*You have to be very careful; you can't say that angle 4 is 35 degrees.*1620

*OK, so what can we say? We know that this line segment right here is parallel to this line right here.*1626

*I can say that the measure of angle 5...because look at this: this angle 5 and angle 2 are alternate interior angles;*1641

*now, let's see if we can apply the theorem and say that they are congruent.*1658

*Here is my transversal; here are the two lines that the transversal is intersecting; are the two lines parallel?*1663

*Yes, they are parallel; now, ignore this side and this side, AD and AE, because you don't need them.*1671

*It is as if they are not even there; cover it up.*1681

*Angle 5 doesn't involve those lines; angle 2 doesn't involve those lines.*1684

*So, all you have to see is this right here; here is BC; there is angle 5 and angle 2.*1690

*Here, these are parallel; here is 5, and here is 2.*1700

*So then, these are alternate interior angles, and they are congruent, because their lines are parallel.*1708

*The measure of angle 5 would be 43.*1716

*And then, from here, I can say that the measure of angle 7...if you look at angle 7 and angle 1, I have a transversal;*1721

*there is my angle 7, and there is my angle 1; these two lines are parallel.*1752

*See how it is only involving the three lines, this line, this line, and this line.*1760

*Ignore BE; see how I didn't draw it, because it is not involved.*1766

*Ignore all of the other lines; just look at those three lines for angle 1 and angle 7.*1769

*If it helps, you can draw it again; this one is a little bit hard to see using this diagram,*1774

*so if it helps you like this, then just draw it again, just using those three lines.*1779

*Angle 7 and angle 1 are corresponding; and since the lines are parallel, I can use the postulate to say that angle 1 and angle 7 are congruent.*1785

*So, the measure of angle 7 is 61.*1794

*So then, the ones that I found: this is 43; this is 61.*1799

*OK, to find the measure of angle 4, I can say that, because all these three angles right here form a linear pair,*1807

*that the measure of angle 7 plus the measure of angle 5 plus the measure of angle 4--they are all going to add up to 180,*1824

*because they form a straight line; all three angles right here are going to form a 180-degree angle.*1833

*You can say that the measure of angle...not 1....4, plus 61, plus 43, equals 180.*1844

*The measure of angle 4, plus 104, equals 180; you subtract the 104, so the measure of angle 4 equals 76; here is 76.*1861

*All of this is the one that I found, so I will write this in red: 76.*1890

*And then, let's look at some other ones: now, if you look at angle 8, angle 8 also involves this parallel line.*1895

*But this one is a little bit harder to see, because you have angle 8 like that; what is this angle right here?*1915

*This is angles 2 and 3 together; it is this angle and this whole thing.*1930

*Now, ignore this line; you are just involving this line, this transversal, and this bottom line DE.*1936

*So, this BE is not there; so it would just be this whole angle together.*1946

*So then, see how this angle right here and this angle right here are corresponding.*1954

*But this has another line coming out of it like this to separate it into angles 2 and 3.*1961

*All I have to do is add up angles 2 and 3, and that is going to be my angle 8.*1970

*This is going to be 78 degrees, and since the lines are parallel, the corresponding postulate says that they are congruent; that equals 78.*1975

*I will write that here: 78; and then, this 78 and angle 6 are going to form a linear pair.*1993

*Right here, 78 +...now, since this is angle 6 right here, you can look at angle 6 and this angle right here,*2013

*78 degrees, because that is angles 2 and 3 combined; they are going to be consecutive interior angles.*2029

*And they are supplementary; so you can just do angle 6 + 78 = 180, which is the same thing as looking at this.*2038

*These are supplementary, so angle 6 and angle 8 (78) are going to add up to 180.*2049

*It is the same thing: the measure of angle 6, plus 78, is going to equal 180.*2055

*The measure of angle 6: if I subtract 78, then you get 102, so this is 102.*2070

*Now, with angle 9, to find the measure of angle 9, that is actually going to involve using the triangles,*2088

*because the only relationship that this angle has with any of the other angles is that it forms within the triangle.*2099

*And see how angle 9 is not supplementary; it doesn't form a linear pair; there is no transversal involved with angle 9.*2111

*It is just these two angles, or those two right there.*2120

*Angle 9 is actually going to involve what is called the triangle sum theorem, where the three angles of a triangle are going to add up to 180.*2125

*So, we haven't gone over that yet; if you want, you can just say that the measure of angle 9, plus 61 (this angle),*2134

*plus the 78, is going to equal 180, and then find the measure of angle 9 that way.*2146

*You can also look at this big triangle and say that this angle, plus this angle, plus this angle, are going to add up to 180.*2151

*You can also look at it as this triangle right here, saying the measure of angle 9 plus 75, together, and then 3, are going to be 180.*2163

*And then, find the measure of angle 9 that way.*2175

*So, for now, we are just going to solve for these; and that is it for this problem.*2179

*The last example: Find the values of x, y, and z.*2186

*Here you have three lines: now, these three lines are going to be parallel.*2192

*I am going to make them parallel, so that I can solve for these values.*2199

*Now, the only angle that is given is right here, 118.*2203

*If you look at this, again, we have four lines involved; and to form special angle relationships, you only need three lines.*2209

*You need the transversal and the two lines that it intersects to form those pairs of angles.*2219

*Whichever lines you are using, always keep them in mind, and then look at what line you are not going to use,*2228

* and ignore that line, since we have four and we only need three.*2238

*Using this angle right here, 118, I can say that now this one right here and 11z + 8 are corresponding.*2245

*And then, this one right here and this one right here are alternate exterior angles, because it is involving these three lines, and not this one right here.*2262

*These would be alternate exterior angles.*2273

*Or, if I ignore this middle line, and I just say that this transversal with this line and this line*2276

*(again, ignoring the middle line--pretending it is not there), then 118, this angle right here, with x, would be alternate exterior angles.*2290

*Imagine if you have a line, a line...here is your transversal; the middle line is not there; this is x, and then this is 118.*2303

*You see that it is alternate exterior angles.*2314

*So then, I can say that x is equal to 118, because the lines are parallel.*2319

*And so then, I can apply the alternate exterior angles theorem, saying that that relationship, that pair, is congruent.*2325

*The next one: let's look at z; this one right here, 11z + 8, is going to equal 118.*2337

* Why?--because, if I look at this line, with this line and this transversal, they are going to be corresponding angles.*2346

*And then, since the lines are parallel, the corresponding angles postulate says that they are congruent.*2358

*11z + 8 = 118; so if you subtract the 8, 11z = 110; z = 10.*2366

*There is my x; there is my z; and then, I have to find y now.*2387

*For my y, I can say that this angle with 118--they are not congruent, remember, because they are going to form a linear pair.*2392

*They form a line, so they are going to be supplementary.*2407

*You can also note that this angle is 118, remember, because we said that they were corresponding--this one with this one.*2412

*So, since this is 118, this angle with this angle would be consecutive interior angles.*2421

*And if the lines are parallel, then the theorem says that they are supplementary, not congruent.*2430

*So, either way, 3y + 2 =...not 180; you have to say that this whole thing, plus the 118, is going to equal 180.*2436

*3y + 2 = 62, and then, if you subtract the 2, then 3y is going to equal 60; y is going to equal 20.*2456

*x is 118; y is 20; and z is 10; just remember to keep looking for those relationships between the pairs.*2474

*You can also definitely use the linear pair, if they are supplementary; you can definitely use that.*2482

*If they are vertical, definitely use that, because you know that vertical angles are congruent.*2490

*So, any of those things--you have a lot of different concepts that you learn that will help you solve these types of problems.*2499

*That is it for this lesson; thank you for watching Educator.com.*2510

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Post by Khanh Nguyen on May 6, 2015

I think question 1 in "Practice Questions" needs to be more specific.

It asks nothing about postulates.

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Post by Jeremy Cohen on August 27, 2014

One of the practice questions says that 180-125=65. This is incorrect, it's like three or four questions in. Please correct

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Post by reid brian on February 7, 2012

ah yeah very good yeah

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Post by Ahmed Shiran on June 7, 2011

Interesting ! :-)