Question

Two angles are complementary. If the larger angle is twice the measure of a smaller angle, then smaller is _____

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

Let, $\alpha$ be the larger angle and $\beta$ be the smaller angle.

if, two angles are complementary then their sum is equal to ${90}^{\circ }$

So, $\alpha +\beta ={90}^{\circ }$ $..........\left(1\right)$

According to question,

$\alpha =2\beta$ $............\left(2\right)$

So, $2\beta +\beta ={90}^{\circ }$ (from eqn$\left(1\right)$ and eqn$\left(2\right)$)

or, $3\beta ={90}^{\circ }$

or, $\beta ={30}^{\circ }$

Therefore, the smaller angle $={30}^{\circ }$

Option $A$ is the correct answer.