Question

If an angle is ${60}^o$ less than two times of its supplement, then the greater angle is

• A. ${100}^o$
• B. ${80}^o$
• C. ${60}^o$
• D. ${120}^o$

Answer 1

The correct option is A ${100}^o$

Option (a) is correct.

Let an angle be $x$ and ${180}^o-x$ be supplementary angles.

So, according to question,

$\Rightarrow x=2({180}^o-x)-{60}^o$

$\Rightarrow x={360}^o-2x-{60}^o$

$\Rightarrow x+2x={300}^o$

$\Rightarrow 3x={300}^o$

$\Rightarrow x=\frac{{300}^o}{3}$

$\Rightarrow x={100}^o$

$\Rightarrow {180}^0-x={80}^0$

Greater angle $={100}^0$

Hence, option $A$ is correct