Question

An angle is equal to one-third its complement. Find the angle's measure.

Answer 1

Hello from MrBillDoesMath!

Answer: 22.5

Discussion:

An angle and its complement add up to 90 degrees So, if "@" is the angle mentioned in the question, its complement is (90 -@). Per the question

@ = (1/3) (90 - @)

Multiply both sides by 3 to get

3@ = 90 - @

Add @ to each side

4@ = 90

Divide each side by 4

@ = 90/4 = 22.5

(and the complementary angle is 67.5)

Regards, MrB