SOLUTION: two angles are complementary. the larger angle exceeds three times the smaller by 38°. what is the measure of each angle?

Algebra ->  Angles -> SOLUTION: two angles are complementary. the larger angle exceeds three times the smaller by 38°. what is the measure of each angle?      Log On


   

Question 1188611: two angles are complementary. the larger angle exceeds three times the smaller by 38°. what is the measure of each angle?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Two angles are called complementary when their measures add to 90°.
let the larger angle be alpha and the smaller angle beta

alpha%2Bbeta=90 ..........eq.1

if the larger angle exceeds three times the smaller by 38°, we have

alpha=3beta%2B38 .........eq.2

substitute alpha in eq.1

3beta%2B38%2Bbeta=90 ..........eq.1, solve for beta
4beta=90-38
4beta=52
beta=13°

go to
alpha=3beta%2B38 .........eq.2, substitute beta
alpha=3%2A13%2B38
alpha=77°