If the supplement of an angle is three times its complement, find the angle.

Given:

The supplement of an angle is three times its complement.

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 $=90^o-x$

The measure of the supplementary angle $=180^o-x$

According to the question,

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

$180^o-x=270^o-3x$

$3x-x=270^o-180^o$

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

$x=45^o$

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