Question

How many degrees are there in an angle which equals two-third of its complement?

• A. ${36}^{\circ }$
• B. ${45}^{\circ }$
• C. ${48}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

Answer: (A)

${36}^{\circ }$

Given, an angle is equal to two-third of its compliment.

Let that angle be $A$.

Therefore, $\angle A=\frac{2}{3}(90-\angle A)$
$\Rightarrow 3\angle A=180-2\angle A$
$\Rightarrow 5\angle A=180$

$\Rightarrow \angle A={36}^{\circ }$