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

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

### Angles of a Triangle

#### Related Links

- All triangles have three angles, and the three angles in a triangle add up to 180 degrees

### Angles of a Triangle

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
- Angles of a Triangle 0:05
- All Triangles Have Three Angles
- Measure of Angles
- Extra Example 1: Find the Missing Angle Measure 5:39
- Extra Example 2: Angles of a Triangle 7:18
- Extra Example 3: Angles of a Triangle 9:24

### Basic Math Online Course

### Transcription: Angles of a Triangle

*Welcome back to Educator.com.*0000

*For the next lesson, we are going to go over angles of a triangle.*0002

*Remember a triangle is a polygon with three sides; three straight sides.*0009

*Which means that there are three angles; those sides form three angles.*0015

*All triangles have three angles.*0021

*Here is one; here is another one; there is a third.*0027

*To name this angle here, we can say angle BAC.*0031

*That would be this angle right here; angle BAC.*0040

*But since the A is a vertex and there is only one angle*0045

*that this is a vertex for, we can just call this angle, angle A.*0052

*This one, I can just call angle B; this is angle C.*0059

*Again only if the point A is a vertex for just a single angle.*0065

*Let me give you an example of what it is not.*0071

*If I have an angle like that, I have two adjacent angles; this is A.*0075

*I can't call this angle, angle A, because there is three different angles formed here.*0084

*There is this small angle; there is this angle; there is this big angle.*0089

*This point, this vertex, is a vertex for three different angles.*0095

*In this case, you cannot call it angle A; you can't say angle A.*0099

*You would have to name the other three points like this one.*0106

*You would have to name, if this is B and this is C, then you have to say angle BAC or like that.*0110

*But again this one, because in a triangle, there is only three angles and three vertex.*0119

*You can just name this as angle A.*0129

*If I say angle A, I am talking about this angle here; angle B; angle C.*0131

*Within the three angles of a triangle, remember each angle has an angle measure, the number of degrees.*0139

*All three angle measures is going to add up to 180,*0148

*like the supplementary angles where we have two angles that form a straight line.*0152

*That adds up to 180.*0156

*Here the three angles of a triangle also add up to 180.*0159

*If this is 60, this is 60, then what I can do is add these two up and subtract it from 180.*0168

*Here if I want to write an equation, I can say measure of angle A.*0179

*Remember this M is for measure; it is to show the number of degrees.*0186

*Measure of angle A plus the measure, the number of degrees, of angle B*0190

*plus the measure of angle C is going to equal 180 degrees.*0199

*We know what the measure of angle A is; how many degrees is angle A?*0212

*We know it is 60; this whole thing is just 60 degrees.*0216

*Measure of angle A is just 60; I can just replace this with 60.*0221

*Do I know measure of angle B?--no; I can just leave that there.*0225

*Plus the measure of angle C is also 60.*0231

*That is all going to add up to 180.*0236

*Again I can just add these two together which is this and this.*0240

*That is going to be 120; plus this unknown adds to 180.*0244

*I can subtract this from 180; 180 minus these two; whatever is left over.*0256

*From the 180 total, if I add these two together*0263

*and then figure out how many degrees are left over from the 180,*0269

*then all of that, all of those left over degrees have to go to angle B.*0273

*I am going to subtract; measure of angle B is going to be 60 degrees.*0278

*The leftover degrees from the 180 is 60; then this also has to be 60.*0290

*That is how you are going to solve for the missing angle measure.*0300

*Remember if we are going to be solving for the missing angle measure,*0305

*then we have to know two of the three angle measures.*0309

*I can't only have the measure of angle A and then find both B and C*0317

*because they are going to be different angles; they could be different angle measures.*0323

*I don't know how many are going to go here and how many are going to go here.*0330

*To find the missing angle measure, you have to have two out of the three like this one.*0334

*I have measure of angle A, 70 degrees.*0343

*I have the measure of angle B; that is 60 degrees.*0348

*I want to find the measure of angle C, meaning I want to find how many degrees is in angle C.*0352

*Again I can just take these two, add them together; how many from the 180?*0359

*I know that this plus this plus this all have to add up to 180.*0364

*This and this are used up.*0371

*However many are left over all have to go to angle C.*0373

*I can say 70 degrees plus this 60 plus the measure of angle C.*0379

*This is the proper way to write it.*0387

*I can't just write C because you are talking about the measure, meaning how many degrees.*0389

*It is all going to add up to 180.*0394

*Again I am going to add these two together.*0398

*This will be 130 plus the measure of angle C.*0400

*130 being used up plus the leftovers is going to equal 180.*0410

*Remember I subtract 180 with this number.*0415

*That way measure of angle C is going to be 50 degrees.*0422

*That means this has to be 50.*0426

*60 plus 70 plus 50 is going to add up to 180.*0429

*That is the missing angle measure.*0434

*Determine the angle measures if the angle measures could be the angle measures of a triangle.*0441

*Three angle measures for the three angles of a triangle.*0448

*If they add up to 180, then they can be the correct angle measures of a triangle.*0455

*But if not, if they don't add up to 180,*0460

*that means they can't be the three angle measures of a triangle.*0462

*The first one, I am going to take 50 plus the 90 plus the 40.*0466

*Just add them all up; I know that 0 plus 0 plus 0 is 0.*0473

*5 plus 9 is 14; plus 4 is 18; yes, they add up to 180.*0479

*That means these three angle measures can be the angle measures of a triangle.*0489

*This one is yes.*0497

*The next one, 45 plus 48 plus the 95.*0504

*5 plus... you can add this 5.*0516

*5 plus 5 is 10; plus 8 is 18; put up the 1; 8.*0520

*Already I know that it is not going to add up to 180*0528

*because the last digit has to be 0 and it is not.*0533

*This is 1 plus 4 is 5; plus 4 is 9; that plus 9 is 18.*0537

*This is 188; this is too much.*0546

*That means it can't be the angles of a triangle; this one is no.*0550

*Remember the angles of a triangle have to add up to 180.*0557

*The third example, find X.*0565

*We want to find the measure of this angle right here.*0568

*I have this triangle.*0574

*Remember all three angles of a triangle have to add up to 180.*0578

*But this one is what I am looking for; this is the missing angle measure.*0583

*I don't have this angle measure either.*0586

*If I need to find the third angle measure, I need to have the other two.*0589

*I have this one; I need to have this one also.*0594

*If I don't have this, then I don't know how many goes here.*0598

*I need to find this one first.*0603

*I have to use another method to find this angle measure.*0606

*I know that this right here, this straight line...*0615

*This is from the last lesson, the previous lesson on angles and lines.*0621

*If this is the line here, this one doesn't have an arrow.*0629

*Just do that; here is where it goes up.*0635

*Remember this, two angles right here, they are adjacent angles.*0643

*But they are also supplementary because it is a straight line.*0652

*It is straight; a straight line has an angle measure of 180.*0656

*This whole thing together is 180; that means this one plus this one is 180.*0662

*This is given that it is 135 degrees.*0671

*If this one together with this small one is 180, then I can just subtract it.*0675

*180 minus the 135 to see what this angle measure is going to be.*0680

*180 minus 135; this is going to be 45 degrees.*0686

*That means this has to be 45 because again this angle with this angle together forms a straight line.*0698

*That has to be 180; they are supplementary angles.*0705

*Now that I found this angle and I have this angle, I need to find the measure of this angle.*0711

*I can just say that X... this is just angle measure so I can just leave it as X.*0719

*I don't have to say measure of angle X because that is not a name.*0728

*That is the number of degrees.*0732

*X degrees plus 53 degrees plus 45 degrees all add up to 180 degrees.*0734

*See how they are all in degrees.*0745

*Again I am going to add these two together to see how many of the 180 I am using up.*0749

*Then see how many are left over to be X.*0753

*This is 53 plus 45 is 98 degrees.*0761

*That means X degrees, this many degrees, plus 90 degrees together is 180 degrees.*0768

*Again I am going to subtract this from 98; I get 82 degrees.*0778

*Right here, X is 82 degrees; this has to be 82.*0796

*That way this plus this plus this, the three angles of a triangle, are going to add up to 180.*0804

*That is it for this lesson; thank you for watching Educator.com.*0812

0 answers

Post by hani shuman on April 4 at 05:44:51 PM