Question

If an angle is double its complement, the angle measures ___

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$

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

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

Given Angle = 2 (Complement)

$x^{\circ }=2({90}^{\circ }-x^{\circ })x^{\circ }=180-2x3x^{\circ }={180}^{\circ }{x}^{\circ }={60}^{\circ }$

Verification Angle = ${60}^{\circ }$

Complement $={90}^{\circ }-{60}^{\circ }={30}^{\circ }$

$\therefore$ 2 (Complement) $=2\left({30}^{\circ }\right)={60}^{\circ }=\text{angle}$