Question

An angle is equal to four times its complement. Determine its measure.

Answer 1

Let the measure of the angle is $x^{\circ }$

Then its complement is ${(90-x)}^{\circ }$

Now, the angle is equal to four times its complement.

Then, $x=4(90-x)$

$⟹$ $x={360}^0-4x$

$⟹$ $x+4x={360}^0$

$⟹$ $5x=360$

$⟹$ $x=\frac{360}{5}={72}^{\circ }$.