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### Course: Math (NSDC) - English>Unit 10

Lesson 6: Triangles part 2

# Finding angles in isosceles triangles (example 2)

Sal combines what we know about isosceles triangles and parallel lines with the power of algebra to solve the angles of an isosceles triangle. Created by Sal Khan.

## Want to join the conversation?

• What does angle adjacent mean?
• yes s like that it's means the adjacent is next to one another
• Who's opening the door?!
• I’m assuming it is a robber stalking Sal behind his chair. ;)
(1 vote)
• I really want to do my work, I really do but I cant bring myself to do it, I just feel like watching everything fall apart and not do anything about it, but I know that wont help me. I just wanted to get that out.
• It is ok Rose Sajaev. It happens to me too. Whenever I have that mindset, I breath in and ask myself, what would my mother do? How would she solve this problem? What is her mindset? I think that might help you. I would also recommend talking to a close friend about that. Do you know what else I do? Sometimes I have a flash back then a flash forward. I have a childhood memory in my head triggered by something I hate. Then, there is an image that I will see in the future. I do and I don't hate it. My flash forward images never tell me whenever I might get in trouble. You are not alone; I have a lot of friends who would say the same thing. Talk to me if you want.
• in what job will I have to find the measurement of an x variable. granted I want to be an engineer but when will I be given an equation like this?
• Engineers have to find the equations themselves and be able to solve them. And they will be much, much more advanced than this material.
• I don't get the proofs, can someone explain all of them to me, please? please answer me!
• Okay. Proofs are a way to show that the statement that you put on the paper is true. There are many different types of proofs in geometry that the only ones I can think of from the top of my head is SSS Postulate and SAS Postulate. SSS tells you that if you get a certain number then you can be able to count them as equal. And also the SAS Postulate says that all the sides and angles are equal depending on the number. I hope that answers your question.
• You can split ABC into 2 equal parts with a midpoint E. Then ACE and BCE are equal to x degrees(Remember that the angle of ACB is 2x degrees.) Then you get a right angle ECD. The value of ECD is (x+10)degrees and the value of BCE is x degrees. Since ECD is complementary, you can combine to get 2x+10=90. From here on, x is equal to 40 degrees. Isn't this easier?
• Is this last video of congruency?
• No there are more videos in the section "Theorems Concerning Quadrilayeral Properties."
• My question is an isosceles triangle but it has 3 other numbers on the outside how do i solve for that there are two 7 one 9 and one 80 (the 80 is in the inside) how do i solve for that?
• I am not sure what you are wanting to solve for, but since the video is about angles, it is pretty basic.
IF the 80 is one of the base angles (across from one of the congruent sides), the other base angle is 80 and the third is 180-(80+80)=20 degrees for the vertex angle (between the two congruent sides).
If 80 is the vertex angle, 80+x+x=180, subtract 80 and combine like terms to get 2x=100, divide by 2 to get each base angle is 50 degrees.
In both cases, the principal is that if you have congruent sides, the two angles opposite the congruent sides (called base angles) have to be congruent also.
• Why couldn't Sal just use alternate angles?
• You could use alternate angles to solve for x. When parallel lines get crossed by another line (which is called a Transversal) you can always use Corresponding Angles, Consecutive Interior Angles or Atlernate angles to solve for x.
• Couldn't you also drop a straight line from C, to create a perpendicular bisector with both line CD and AB. And when you dropped the line from C than you divide the 2x because you are cutting it in half, and then (2x/x) + (x + 10) = 90º and than that simplifies down to x = 40º

## Video transcript

So what do we have here? We have a triangle, and we know that the length of AC is equal to the length of CB. So this is an isosceles triangle, we have two of its legs are equal to each other. And then they also tell us that this line up here, they didn't put another label there. Let me put another label there just for fun. Let's call this, you could even call this a ray because it's starting at C, that line or ray CD is parallel to this segment AB over here, and that's interesting. Then they give us these two angles right over here, these adjacent angles. They give it to us in terms of x. And what I want to do in this video is try to figure out what x is. And so given that they told us that this line and this line are parallel, and we can turn this into line CD, so it's not just a ray anymore, so it just keeps going on and on in both directions. The fact that they've given us a parallel line tells us that maybe we can use some of what we know about transversals and parallel lines to figure out some of the angles here. And you might recognize that this right over here, this line-- let me do that in a better color. You might recognize that line CB is a transversal for those two parallel lines. Let's let me draw both of the parallel lines a little bit more so that you can recognize that as a transversal, and then a few things might jump out. You have this x plus 10 right over here, and its corresponding angle is right down here. This would also be x plus 10. And if this is x plus 10, then you have a vertical angle right over here that would also be x plus 10. Or you could say that you have alternate interior angles that would also be congruent. Either way, this base angle is going to be x plus 10. Well, it's an isosceles triangle. So your two base angles are going to be congruent. So if this is x plus 10, then this is going to be x plus 10 as well. And now we have the three angles of a triangle expressed as functions of-- expressed in terms of x. So when we take their sum, they need to be equal to 180, and then we can actually solve for x. We get 2x plus x plus 10 plus x plus 10 is going to be equal to 180 degrees. And then we can add up the x's. So we have a 2x there plus an x plus another x, that gives us 4x. 4 x's. And then we have a plus 10 and another plus 10, so that gives us a plus 20, is equal to 180. And we can subtract 20 from both sides of that, and we get 4x is equal to 160. Divide both sides by 4, and we get x is equal to 40. And we're done. We've figured out what x is, and then we could actually figure out what these angles are. If this is x plus 10 then you have 40 plus 10, this right over here is going to be a 50-degree angle. This is 2x, so 2 times 40, this is an 80-degree angle. It doesn't look at it the way I've drawn it, and that's why you should never assume anything based on how a diagram is drawn. So this right over here is going to be an 80-degree angle, and then these two base angles right over here are also going to be 50 degrees. So you have 50 degrees, 50 degrees, and 80, they add up to 180 degrees.