If the complement of an angle is equal to the supplement of the thrice of it. Find the measure of the angle.

Given:

The complement of an angle is equal to the supplement of the thrice of it.

To do:

We have to find the measure of the angle.

Solution:

Two angles are said to be supplementary if the sum of their measures is $180^o$.

Two angles are said to be complementary if the sum of their measures is $90^o$.

Let the required angle be $x$.

This implies,

The measure of the complementary angle $=90^o-x$

Thrice of the required angle $=3x$

The measure of the supplement of the thrice of it $=180^o-3x$

According to the question,

$90^o-x=180^o-3x$

$3x-x=180^o-90^o$

$x=\frac{90^o}{2}$

$x=45^o$

The measure of the required angle is $45^o$.