Question

A complement of an angle measures 10 degrees more than the measure of the angle. What is the measure of the angle and its complement? Explain your reasoning.

Answer 1

Compelemttry angles add to 90
angles are x and y
x+y=90

x is 10 more than y
x=10+y
sub

10+y+y-90
10+2y=90
minus 10
2y=80
divide 2
y=40

sub back
x=10+y
x=10+40
x=50

numbers are 40 and 50 degrees

Answer 2

The angle is 40 degrees and its complement is 50 degrees. Complementary angles add up to 90 degrees. You know the angle is 40 degrees because 40 is the only angle measure that has a complement 10 more than itself.