Question

The measure of an angle is five times its complement. The angle measures

(a) ${25}^{\circ }$

(b) ${35}^{\circ }$

(c) ${65}^{\circ }$

(d) ${75}^{\circ }$

Answer 1

The correct option (d) ${75}^{\circ }$

Let the measure of the required angle be $x.$

Then, the measure of its complement will be $90-x.$

According to the question, we have

the measure of angle $=$ 5$\times$(its compliment)

$\Rightarrow x=5(90-x)$

$\Rightarrow x=450-5x$

$\Rightarrow 6x=450$

$\therefore x={75}^{\circ }$

so, the angle is ${75}^{\circ }$.