SOLUTION: Hello, I could really use some help solving this word problem I have on my homework. The word problem is: "In triangle XYZ, angles X and Y have the same measure. The sum of the

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hello, I could really use some help solving this word problem I have on my homework. The word problem is: "In triangle XYZ, angles X and Y have the same measure. The sum of the      Log On

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Question 665186: Hello,
I could really use some help solving this word problem I have on my homework. The word problem is:
"In triangle XYZ, angles X and Y have the same measure. The sum of the measure of angles Y and Z is 100°. How many degrees are there in each of the three angles?"
So far, I have written down that
X = Y
and
Y + Z = 100°. I know that all the angles in a triangle add up to 180° so I know that my equation will = 180°.
I'm having trouble coming up with an equation to solve this problem. Once I get that, I can finish the rest of the poem easily.
Thank you for your help in advance!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
angles X and Y have the same measure;...=> X=Y
The sum of the measure of angles Y and Z is 100°...=> Y%2BZ=100

the sum of all angles in a triangle is:
X%2BY%2BZ=180...since X=Y and Y%2BZ=100, we have
Y%2B100=180
Y=180-100
highlight%28Y=80%29
we know that X=Y, so highlight%28X=80%29 too
now find Z
Y%2BZ=100
80%2BZ=100
Z=100-80
highlight%28Z=20%29