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Angles of a Triangle

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  • 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

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 angle0045

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 B0190

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 together0263

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 C0317

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 1800528

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