Question

The measure of an angle is fives times its complement. The angle measure:

• A. $25°$
• B. $65°$
• C. $35°$
• D. $75°$

Answer 1

The correct option is D

$75°$

Complementary angles:

Two angles are called complementary if the sum of their measures is 90^o.

Let the measure of the angle be $x$

Then, the measures of a complement angle be $90°-x$.

Finding the value of x.

If the measure of an angle is five times its complement then we can write;

$$\begin{gathered} x=5(90°-x) \\ x=450-5x \\ 6x=450 \\ x=\frac{450}{6}=75° \end{gathered}$$

So, the measure of the angle be $75°$.

Hence, the correct option is (D).