SOLUTION: Two angles are complementary. The measure of the larger angle is 10 more than 4 times the measure of the smaller angle. Find the measure of both angles.

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Question 1152103: Two angles are complementary. The measure of the larger angle is 10 more than 4 times the measure of the smaller angle. Find the measure of both angles.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by MathLover1(20850) About Me  (Show Source):
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complementary angles are two angles whose sum is 90 degrees
let the larger angle be alpha and the smaller angle beta
alpha%2Bbeta=90.......eq.1
if the measure of the larger angle is 10 more than 4 times the measure of the smaller angle, we have
alpha=4%2Abeta%2B10........eq.2-> substitute in eq.1
4%2Abeta%2B10%2Bbeta=90.......eq.1
5%2Abeta=90-10
5%2Abeta=80
beta=80%2F5
beta=16 degrees
then
alpha%2Bbeta=90.......eq.1
alpha%2B16=90
alpha=90-16
alpha=74