Question

Can there be a pair of complementary angles such that both of them are equal? If yes, find the values of those angles.

• A. Insufficient data
• B. Yes, ${30}^{\circ }$
• C. Yes, ${45}^{\circ }$
• D. No, there exists no such pair of angles.

Answer 1

The correct option is C Yes, ${45}^{\circ }$

Let the measure of each angle be x.
Since the angles are complementary, their sum will be 90°.
$\Rightarrow x+x={90}^{\circ }$
$\Rightarrow 2x={90}^{\circ }$
$\Rightarrow x={45}^{\circ }$
$\therefore$ It is possible to have a pair of equal angles that are complementary and measure of each of them will be ${45}^{\circ }$.