Question

Tick ($\surd$)the correct answer in each of the following:

If an angle is $4$ times its complement, what is the angle?

• A. (a)$72°$
• B. (b)$108°$
• C. ©$144°$
• D. (d)$36°$

Answer 1

The correct option is A

(a)$72°$

Complementary angles are angles whose sum is equal to $90°$

Let one complementary angle be $x$

Then,angle is $4$ times its complement$=4x$

Then, $$\begin{gathered} 4x+x=90° \\ 5x=90° \\ x=\frac{90°}{5}=18° \end{gathered}$$

$4x=4\times 18°=72°$

Hence,angle $4$ times its complement is $72°$.