Question

Find the measure of the angle which is double of its complementary angle.

• A. $60°$
• B. $30°$
• C. $45°$
• D. $120°$

Answer 1

The correct option is A

$60°$

The explanation for the correct option

Let us assume that the angle is $x$.

As the angle is double its complementary angle, so complementary angle $=\frac{x}{2}$.

As per the definition of complementary angles, the sum of the considered angle and its complementary angle is $90°$.

Thus, $x+\frac{x}{2}=90°$

$$\begin{gathered} \Rightarrow \frac{2x+x}{2}=90° \\ \Rightarrow 3x=180° \\ \Rightarrow x=\frac{180°}{3} \\ \Rightarrow x=60° \end{gathered}$$

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