SOLUTION: An angle measures 46° more than the measure of a complementary angle. What is the measure of each angle? Thanks

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Question 1078656: An angle measures 46° more than the measure of a complementary angle. What is the measure of each angle? Thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Two angles are complementary when they add up to 90 degrees.
let's angle be alpha and its complementary angle beta
alpha%2Bbeta=90=>alpha=90-beta....eq.1
given:
an angle measures 46° more than the measure of a complementary angle
so, alpha measures 46° more than beta=>
alpha=beta%2B46........eq.2
from eq.1 and eq.2 we have
90-beta=beta%2B46
90-46=beta%2Bbeta
44=2beta
44%2F2=beta
highlight%28beta=22%29°
find alpha
alpha=90-beta....eq.1
alpha=90-22
highlight%28alpha=68%29°