For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### 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

### Basic Math Online Course

### Transcription: Intersecting Lines and Angle Measures

*Welcome back to Educator.com.*0000

*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 lines*0119

*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 degrees*0356

*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 angles*0690

*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 are*0851

*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 Educator.com.*1455

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.