Question

The measure of the complementary angle and the supplementary angle of a given angle are
$x$
° and
$4x$
° respectively. What is the measure of the given angle?​

Answer 1

Let that angle be y, whose complementary angle is x° and supplementary angle 4x°

Then, x=90°-y-----------------(1)

and 4x=180°-y-----------------(2)

Substituting equation (1) in (2)

4(90°-y)=180°-y

360°-4y=180°-y

180°=3y

y= 60°

x=90°-y

x=90°-60°=30°

and 4x=180°-y

4x=180°-60°=120°

Also, 4x=4×30°=120°

Therefore, the measure of the given angle is 60°.

Hope it helps you.