SOLUTION: An angle measures 15 degrees more than its complement, Find the measure of two angles.

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Question 665529: An angle measures 15 degrees more than its complement, Find the measure of two angles.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

complementary angles are angles whose measures sum to 90°

let alpha be an angle, and beta be its complement, then
alpha%2Bbeta=90......1
and if an angle measures 15 degrees more than its complement, we have:

alpha=beta+%2B15.......2...plug it in equation 1
beta+%2B15%2Bbeta=90......1..solve for beta
2beta+=90-15
2beta+=75
beta+=75%2F2
highlight%28beta+=37.5%29
now find alpha

alpha=beta+%2B15.......2

alpha=37.5+%2B15
highlight%28alpha=52.5%29