Question

Find the angles in each of the following.
The angle which is two times its complement

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${30}^{\circ }$
• D. None of these

Answer 1

Answer: (A)

${60}^{\circ }$

Two Angles are Complementary when they add up to 90 degrees.

Let the $\angle B$ is complement of $\angle A$

Now according to question $\angle A=x$ then $\angle B=2x$

Hence $\angle B+\angle A=x+2x={90}^o$

$⟹3x={90}^o⟹x={30}^o$

$\angle A={30}^o$ and $\angle B={60}^o$

Since $\angle B$ is $2$ times its complement $\angle A$.

So the angle which is two times its complement ${60}^o$.