SOLUTION: In triangle ABC, angle A and B have the same measure. Angle C is 90 degrees larger than both A and B. What are the measures of the 3 angles? Totally lost. Please help me out. Than

Algebra ->  Points-lines-and-rays -> SOLUTION: In triangle ABC, angle A and B have the same measure. Angle C is 90 degrees larger than both A and B. What are the measures of the 3 angles? Totally lost. Please help me out. Than      Log On


   

Question 171141: In triangle ABC, angle A and B have the same measure. Angle C is 90 degrees larger than both A and B. What are the measures of the 3 angles? Totally lost. Please help me out. Thanks a bunch.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
,font size=4>
We know that A%2BB%2BC=180, EQN 1
But, A=B
Also ---->+system%28C=A%2B90%2CC=B%2B90%29 ---> Angle C is 90 deg larger right?
subst. one of this condition in EQN 1:
A%2BB%2Bhighlight%28A%2B90%29=180
Remember too ----> A=B, therefore,
A%2Bhighlight%28A%29%2Bhighlight%28A%2B90%29=180
3A=180-90
3A=90 -------> cross%283%29A%2Fcross%283%29=cross%2890%2930%2Fcross%283%29
highlight%28A=30%5Eo=B%29
Then, C=30%5Eo%2B90%5Eo=highlight%28120%5Eo=C%29
Check as per EQN 1:
30%5Eo%2B30%5Eo%2B120%5Eo=180%5Eo
180%5Eo=180%5Eo
Thank you,
Jojo