Question

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

Answer 1

Answer: $81^{\circ}\ \text{ and }\ 9^{\circ}$

Step-by-step 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

$x+x-72=90\\\\\Rightarrow\ 2x=90+72\\\\\Rightarrow\ 2x=162\\\\\Rightarrow\ x=\dfrac{162}{2}=81$

Therefore, the measure of angles are :

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

Answer 2

Complementary angles: Two angles that add to 90 degrees

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