For more information, please see full course syllabus of Basic Math
For more information, please see full course syllabus of Basic Math
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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
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 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
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Post by hani shuman on April 4, 2017