Question

Find the measure of an angle which is equal to its complement.

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

Answer 1

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

Let the angle $=x^{\circ }$

$\therefore$ its complement = ${90}^{\circ }-x^{\circ }$

It is given that, $x^{\circ }={90}^{\circ }-x^{\circ }$

$2x={90}^{\circ }$

$x={45}^{\circ }$

Verification Angle $={45}^{\circ }$

Complement = ${90}^{\circ }-{45}^{\circ }$

$={45}^{\circ }$