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Lecture Comments (3)

0 answers

Post by Rowena Vittali on August 24, 2015

How to find and compare the measure of the angles?

1 answer

Last reply by: Professor Pyo
Thu Jan 2, 2014 4:18 PM

Post by David Martinuk on December 3, 2013

wouldn't angle 3 and angle 4 be horizontal angles not vertical.

Intersecting Lines and Angle Measures

Related Links

  • Lines are always straight and never ending
  • When two or more lines cross each other, they are intersecting lines
  • An angle has two sides and a vertex
  • The degree of the angle is the angle measure
  • Acute angles are less than 90 degrees
  • Right angles are 90 degrees
  • Obtuse angles are greater than 90 degrees
  • Vertical angles: Two opposite angles formed by intersecting lines
  • Adjacent angles: Angles next to each other and have a common vertex and side
  • Complementary angles: Two angles that add up to 90 degrees
  • Supplementary angles: Two angles that add up to 180 degrees

Intersecting Lines and Angle Measures

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 0:00
  • Intersecting Lines 0:07
    • Properties of Lines
    • When Two Lines Cross Each Other
  • Angles 2:56
    • Properties of Angles: Sides, Vertex, and Measure
  • Classifying Angles 7:18
    • Acute Angle
    • Right Angle
    • Obtuse Angle
  • Angle Relationships 8:56
    • Vertical Angles
    • Adjacent Angles
    • Complementary Angles
    • Supplementary Angles
  • Extra Example 1: Lines 16:00
  • Extra Example 2: Angles 18:22
  • Extra Example 3: Angle Relationships 20:05
  • Extra Example 4: Name the Measure of Angles 21:11

Transcription: Intersecting Lines and Angle Measures

Welcome back to

For the next lesson, we are going to go over intersecting lines and angle measures.0002

Remember a line is always straight and it is never ending.0009

Meaning it goes on forever; that is what these arrows are for.0015

It shows that it is going on forever this way and that way.0017

To name a line, we can use the points that are on the line.0023

To name a line using the points, we need at least two points.0031

Here point A and point B; can write it as A, B.0035

Then you are going to draw a little line above it like that.0045

That shows line AB.0049

Because it doesn't matter which way it is going,0052

whether I name it AB or BA, I am still talking about the same line.0055

It goes on forever in both directions.0063

I can also say BA with a line over it to show that it is a line.0067

This is how you represent, how you name this line.0074

This whole thing is also called L; I can also name this as line L.0081

When you usually name a line, it is usually in cursive.0092

That is why it is a cursive L; line L.0095

Three ways; AB using the points, two points on the line.0098

AB with the line above, AB; or BA, same thing.0104

Or if the whole thing has a name L, then you can just call it line L.0110

When you have two lines that are intersecting or two lines0119

that cross each other like this, they are intersecting lines.0121

They are two lines that intersect; they intersect at point P.0126

This is a point; that is the point where they touch; that is point P.0129

This is line L; line N.0136

For this, you can also name this as line CD; line DC just like we did here.0140

But P is also on that line; I can also name this as line PD; PD with a line above it.0148

That can also be used to name this line; just any two points on that line.0157

If I say line CD or line PD, I am talking about the same line.0164

It doesn't matter which one.0169

Again that is intersecting lines, when they cross each other.0172

For angles, this right here is an angle; B is a point on one side.0178

C is a point on the other side of the angle; there is two sides.0189

This point right here where those two sides meet, that is the vertex.0194

That is called the vertex; point A is the vertex of that angle.0197

When I name this angle, I can say angle; that just shows an angle.0204

I use the points; I need three points on this angle.0211

If I just say BC, then that doesn't tell me what angle I am talking about.0216

Or that doesn't even give me an angle; I have to say BAC; angle BAC.0220

Again if you are going to use points to represent the name of an angle, then you have to use three points.0230

I can also say angle CAB.0239

Make sure your angle is going like that; it is not going like this.0249

If you noticed for these two names, both of these, A the vertex is the middle point.0255

It is BAC; angle CAB; I can't say angle BCA.0263

Angle BCA is not the correct name for it.0269

Angle BCA, that is not a name for this angle.0272

The vertex has to be the middle point when you name it.0278

Another name, just like the previous slide where we had line L,0286

the name of the line was L so we can also name it line L.0292

For this one, if it says 1, usually the angles, if there is a name for it, it is a number.0297

That number 1 right there, that is talking about this angle.0306

So I can also say angle 1.0309

The degree of an angle is the angle measure.0318

Measure is talking about how narrow or how wide open the angle is.0322

This right here, if I say this is a 90 degree angle, it is a perfect right angle.0333

Meaning this is vertical and this is horizontal.0339

This little box right here says that it is a 90 degree angle.0344

This is 90; to represent degree is a little dot right there.0348

That is 90 degrees.0354

If I have a straight line, a straight line measures 180 degrees0356

because it is like 90 and then it is another 90.0367

If I were to draw a 90 degree angle from here, it will be half way.0370

This is 90; this is 90; together it makes 180.0373

If I start from here and I go all the way around a full circle, that is 360.0383

You can also use this to represent a 360.0392

This right here was 180; that is 180.0400

This again is 180; together it is 360.0404

All of it together, the whole full circle going all the way around,0408

from starting point and then going all the way back to that same point, it is 360 degrees.0411

Again right angle is 90.0418

Two right angles make a straight line; that is 180 degrees.0420

Two straight lines, going this way and then going another this way, is 360.0426

That is a full circle; a full circle is always 360 degrees.0430

There is three types of angles when it comes to classifying.0440

The three types would be acute angle... this is when...0444

Remember this is a 90 degree angle; that is a 90 degree angle.0450

Acute angle has to be smaller than a right angle.0458

It has to be smaller than 90; this is less than 90 degrees.0463

That makes up an acute angle.0472

Right angle we know is perfectly 90 degrees.0475

An angle that is greater than 90, greater than 90 degrees, is called an obtuse angle.0484

The right angle would be like that right there; this is 90.0496

It is going more than 90; it has to be bigger than 90.0502

These are the three types of angles.0506

So that you don't confuse the acute angle with the obtuse angle, we know a right angle is perfectly 90.0510

Acute angle and an obtuse angle; notice how the acute angle is a lot smaller than the obtuse angle.0515

Acute angles are small; they are smaller than 90.0521

Think of it as a cute angle because it is small.0524

Acute angles are small; obtuse angles are big; three types of angles.0529

When we compare two different angles to each other, some angles have a relationship.0541

The first angle relationship is a vertical angle.0551

If we have intersecting lines, two lines that are intersecting, there is four angles that are formed.0557

We have this angle, this angle, this angle, and this angle.0564

There is four angles that are formed by intersecting lines.0567

When you look at the opposite angles, the top one and the bottom one, those are called vertical angles.0570

Remember when we talked about how to name angles.0578

This is angle 1; this is angle 2.0582

We can name angles by using the points on the angle.0587

Or if it is labelled as 1, 2, then we can say that that is angle 1 and this is angle 2.0589

This is different; don't get it confused with angle measure.0597

Because angle measure, that is how many degrees that angle is and it has that little degree sign.0599

This is not degrees; it is not 1 degree.0609

It is angle 1; this is angle 2.0611

Angle 1 and angle 2 are vertical angles; that is the relationship between the two.0615

Again if they are intersecting lines and then they are opposite, this one and this one are vertical angles.0620

This one and this one are also vertical angles.0626

If this is angle 3, this is angle 4, then angles 3 and 4 would also be vertical angles.0631

The next type of relationship is called adjacent angles.0638

Adjacent, think of it as next to.0643

They are angles that are next to each other.0647

They have to have a common vertex and side; they share two things.0650

The vertex, we know that a vertex is this part right here.0655

That is the vertex; they have to have the same vertex and a side.0658

Angles 1 and 2 here are adjacent because they are next to each other.0666

This is the vertex of angle 1; this is the vertex of angle 2.0671

They have the same vertex; and they share a side.0675

This is the side that they share; these would be adjacent angles.0679

Adjacent angles don't always have to be from intersecting lines.0686

If I have let's say like this, angles 1 and 2, these would be adjacent angles0690

because they share the same vertex and the same side and they are next to each other.0701

Same vertex; same side; angles 1 and 2 here are also adjacent.0708

Complementary angles.0715

Complementary angles are two angles that when you add them together becomes 90.0717

It has to be 90 for it to be complementary.0723

Again two angles that add up to 90 degrees.0727

Here angle 1 and angle 2, if you add them together, it is going to become 90 degrees.0730

If I were to take this angle and place it so that it is like this, this would be angle 1.0737

See how it forms a right angle; 90 degrees is a right angle.0746

Any two angles that add up to 90; they don't all have to be adjacent.0752

It doesn't have to be like this for it to be complementary.0755

I can have one angle here; I can have another angle over here somewhere.0758

As long as they add up to 90 degrees, they would be complementary angles.0767

Supplementary angles are any two angles that add up to 180.0775

Here angle 1 and angle 2 would add up to 180.0782

If I were to put it together, notice how they would line up to be a straight line.0786

This is angle 1; this is angle 2.0796

If you add them together, see how this would be a straight line, 180 degrees.0799

Remember how we said if I have a straight line, it is as if I have two 90 degree angles.0806

This is 90; this is 90; together they add up to 180.0817

A straight line is 180.0822

If I have two angles that form a straight line, then they are supplementary angles.0825

They don't have to be together; they don't have to be adjacent.0834

They can be just like the complementary angles.0838

They can be two angles that are split; one angle here, one angle over there.0841

As long as they add up 180, they are supplementary angles.0847

Again two angles that are opposite to each other when they are0851

formed by intersecting lines are called vertical angles.0855

Angles 1 and 2, since they are opposite angles, they are vertical.0859

Adjacent angles are two angles that are next to each other.0865

They have to share a common vertex and a side.0869

An example of nonadjacent angles, meaning two angles that are not adjacent, would be like that.0873

This is angle 1; this is angle 2.0883

Even though they are next to each other, they are not adjacent because they don't share the same vertex.0886

This is the vertex of angle 1; this is the vertex of angle 2.0892

For this, this is not adjacent.0897

They have to be next to each other and share the same vertex.0901

Complementary angles are two angles that add up to 90 whether they are together, adjacent, or not.0908

Supplementary angles are two angles that add up to 180 whether or not they are adjacent.0916

To remember between complementary and supplementary, C comes before S in the alphabet.0923

C, A-B-C, and then S is way down there; C comes before the S.0932

90 comes before 180 if you were to count; 90 comes before 180.0937

C before S; 90 before 180.0943

C, complementary angles are 90 degree angles; supplementary are 180.0946

That is just one way for you to remember between complementary and supplementary.0953

Our examples, the first one, write two other names for AB, line AB.0961

Line AB is this line right here.0969

To find two other names... I didn't label them; this is L, N, and P.0974

Here I can say, since that is AB, I need to find two other names.0987

I can say BA; line BA; that is one other name.0995

Then I can say line P; line P.1002

Again the names for lines are usually in cursive; line BA and line P.1009

Name two intersecting lines; line AB and line AC are intersecting.1020

Line AB with line DE is intersecting.1030

I can also say line P with line L or line P with line N; any of those.1036

But just make sure that it is not line AC with line DE.1043

They could intersect eventually because remember these lines are never ending.1049

They go on forever; if they are not parallel, eventually they can meet sometime.1053

But in this diagram, it doesn't show them intersecting.1062

We can just say line AB with a line; this one with line maybe DE.1067

You can also say BE; it doesn't matter; DE; any two points on the line.1079

DE; those are two intersecting lines; I can also say line P with line L.1085

Classify each angle and name the relationship between the two.1103

This angle; classify, remember there is three types of angles.1108

The acute angle, a right angle, and obtuse angle; this is less than 90.1111

I know that because a 90 degree angle is a right angle; that is 90.1118

This would be an acute angle.1125

This one is greater than 90; it is 135 degrees.1133

That is definitely greater; this is an obtuse angle.1139

The relationship between these two, I know they are not vertical; they are not adjacent.1147

They are probably either going to be complementary or supplementary.1155

Let's add these up; this one, 45 degrees plus 135 degrees.1158

135 plus 45; 7, 8; they add up to 180 degrees.1169

Because they add up to 180, that would make them supplementary angles.1182

If they were to add up to 90, then that would be complementary angles.1199

The next one, determine the angle relationship between the pair of angles.1206

The first is angle 1 or angle 2.1210

Again be careful that these are not the angle measures.1215

There is no way that this can be 1 degree, 2 degrees.1218

These are the names of the angles.1222

This angle and this angle here, what is the relationship between them?1226

They are next to each other; they share the same vertex and a side.1233

These are adjacent; adjacent angles.1237

The next one, angle 3 and angle 4, see how they are opposite angles.1247

They are formed by intersecting lines; these are vertical; vertical angles.1254

The fourth example, name the measure of angle 1; here we have a right angle.1274

This angle along with this angle together form that right angle.1284

I want to find the angle of this measure right here.1290

I know this whole thing is 90.1292

If I take 90 and I subtract the 50, don't I get measure of angle 1?1297

I can say the measure of angle 1... a shortcut for me to say that is measure of angle 1.1303

You know angle 1 is like that.1310

But when I am talking about the angle measure, the degrees, then I could put M for measure.1312

This just says measure of angle 1; I am talking about the number of degrees.1320

Measure of angle 1 plus... this is 50 degrees.1327

Together, if I add them together, it becomes 90 degrees.1335

How do I solve for measure of angle 1?--I can subtract 50.1341

That way measure of angle 1 is 40 degrees.1348

This is 40; this is 50; together they add up to 90.1354

We know that these two angles are adjacent because they are next to each other.1360

They share the same vertex and a side.1364

They are also complementary because they add up to 90.1367

This angle with this angle together are complementary angles.1372

Here straight line.1377

That means together measure of angle 1 plus 83 degrees has to add up to 180 degrees.1381

Straight line is always 180.1391

Again I am going to put measure of angle 1 plus...1394

This angle plus this angle, 83 degrees, equals a total of 180 degrees.1400

I am going to subtract the 83 degrees.1411

Measure of angle 1 is... this is 97 degrees.1417

Here these two we know are supplementary because they add up to 180.1434

90 so they are complementary; 180 so they are supplementary.1443

These are also adjacent angles; they are next to each other; same vertex, side; adjacent.1447

That is it for this lesson; thank you for watching