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# Triangle angle challenge problem 2

Find angle measures in triangles when the given measures are algebraic expressions. The key idea is that the sum of all angles in a triangle is always 180 degrees. We can also use parallel lines and transversals to find angle measures. Created by Sal Khan.

## Want to join the conversation?

• I dont understand the second example at all... can someone help?
• He does not tell you one crucial point: B, C, and D are collinear. So the line that contains B, C, and D is a transversal of the two parallel lines, etc.
• I'm having trouble with the star geometry problems. Could someone possibly break them down for me? I want to understand everything well, and that's the only thing giving me trouble.
• Oh, this is going to be hard to explain...
So, apologies if it isn't sufficient for you.
Here is what the problem looks like:
Create an upside-down pentagon.
The point of the pentagon (which is upside down) measures 105 degrees.
Create the star legs stemming from the pentagon. In the bottom left triangle, there is another given angle. It is the farthest angle down, and it measures 39 degrees.
Now to the left of the pentagon, is the angle we are trying to find, X.
(You may be able to find the exercise by just going through "Finding angle measures using Triangles" over and over. That actually may be easier than visualizing it...)
Anyway, to find X, we use some rules that are fundamental to geometry. A straight angle is equal to 180 degrees, specifically.
So, if it gives us 105, we know the angle(s) adjacent to it has to be 75. This is because a straight angle equals 180, adding the two must equal 180.
So we now have 75 degrees and 39 degrees in the bottom left triangle. This equals 114 in total. We know the interior angles of a triangle also equals 180 degrees. So if we already have the 114, that means the angle opposite of X, the vertical angle, is equal to 66. (Vertical angles are always equal to each other, so if one is 66, the other is 66.)
Thus we have solved for X.
I don't know if that helps, but I hope it does.
If you were stuck on another problem or one similar, just ask another question rather than continuing this strand of comments and answers. Anyway, good luck! Hope that helps!
• how do you know the difference between obtuse and scalene triangles?
• How do you know when the angles are congruent?
• I still don't understand how to do it and I'm really stuck on these types of questions so can u go through some more examples with me?
• i didn't understand the 4x thing
• The 4x comes from translating words to Math. the measure of the largest angle (lets call L) is (=) 4 times (multiply) the second largest angle (which has been defined as x). So to translate this into Math, L= 4x.
• So in the first problem he did,why couldnt you substitute 4x for 4y and then do the problem from there?
• The goal is to set up an equation that will allow you to solve for a specific value. If you used 4y, you would get:

4y+x+10=180
4y+x=170

The only way to solve at this point would be to assume that y=x (which we could in fact do, based on the information in the question), then substitute one of the variables (i.e. y for x). Of course this would be the same as using only one variable to begin with:

4y+y=170
5y=170
y=34
• why are supplementary angles equal