# The measure of an angle is 6 less than 5 times its complement. What is the measure of the complement?

Question
Analytic geometry
The measure of an angle is 6 less than 5 times its complement. What is the measure of the complement?

2021-02-07
Two angles are complementary if the sum of their measures is 90°. If x is the measure of the angle, then 90−x is the measure of the complement, both in degrees.
Using the given statement, we can write:
x=5(90−x)−6
Solve for x:
x=450−5x−6
x=444−5x
6x=444
x=74
So, the measure of the complement is 90−74=16°.

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