SOLUTION: In triangle ABC, angles A and B are complementary angles. The measure of angle A is 10° leas than four times the measure of B. Find the measure of all three angles.

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Question 1047512: In triangle ABC, angles A and B are complementary angles. The measure of angle A is 10° leas than four times the measure of B. Find the measure of all three angles.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If A and B are complementary (their measures adding to 90%5Eo ),
then angle C measures highlight%2890%5Eo%29 ,
because the sum of the measures of all three angles in any triangle is 180%5Eo .
If A and B are the measures , in degrees, of angles A and B,
" The measure of angle A is 10° leas than four times the measure of B" translates as A=4B-10 .
Then,
system%28A%2BB=90%2CA=4B-10%29-->system%284B-10%2BB=90%2CA=4B-10%29-->system%285B-10=90%2CA=4B-10%29-->system%285B=90%2B10%2CA=4B-10%29-->system%285B=100%2CA=4B-10%29-->system%28B=100%2F5%2CA=4B-10%29-->system%28B=20%2CA=4B-10%29-->system%28B=20%2CA=4%2A20-10%29-->system%28B=20%2CA=80-10%29-->highlight%28system%28B=20%2CA=70%29%29