Question

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

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

Answer 1

The correct option is A

${100}^{\circ }$

Explanation for correct answer:

Two angles are said to be supplementary if their sum is equal to ${180}^{\circ }$

Let one of the angle be $A$

So, the supplement of $A$is ${180}^{\circ }-A$.

According to the given condition

$A=2({180}^{\circ }-A)-{60}^{\circ }$

$\Rightarrow$ $A={360}^{\circ }-2A-{60}^{\circ }$

$\Rightarrow$$3A={300}^{\circ }$

$\Rightarrow$$A={100}^{\circ }$

So, the other angle will be ${80}^{\circ }$.

Hence $A={100}^{\circ }$ is the greater angle, so option $\left(A\right)$ is the correct answer.