Question

An angle measures 72° less than the measure of a complementary angle. What is the measure of each angle?

Answer 1

Complementary angles: Two angles that add to 90 degrees

Angle a: 90 degrees - 72 degrees = 18 degrees
Angle b: 72 degrees

Answer 2

Answer:
`81^(\circ)\ \text{ and }\ 9^(\circ)`

Explanation:

We know that the sum of two complementary angles is
`90^(\circ)`.

Given : An angle measures 72° less than the measure of a complementary angle.

Let x be the angle , then the measure of other angle will be x-72.

Since they area complementary , then we have

`x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=(162)/(2)=81`

Therefore, the measure of angles are :

`81^(\circ)\ \text{ and }\ (81-72)^(\circ)=9^(\circ)`