Question

If the complement of an angle is equal to the supplement of the thrice of it then the measure of the angle is

• A. ${45}^{\circ }$
• B. ${80}^{\circ }$
• C. ${90}^{\circ }$

Answer 1

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

Let the required angle be $x^{\circ }$
Then its complement angle = ${90}^{\circ }-x$
and supplement of thrice of the angle= ${180}^{\circ }-3x$
$\therefore ({90}^{\circ }-x)={180}^{\circ }-3x\Rightarrow 3x-x={180}^{\circ }-{90}^{\circ }\Rightarrow 2x={90}^{\circ }\Rightarrow 2x={90}^{\circ }\Rightarrow x={45}^{\circ }$
$\therefore$ Required angle = ${45}^{\circ }$