Question

Question 34

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

Let the angle be x, then its supplement will be $({180}^{\circ }-x)$
It is given that, the angle is ${60}^{\circ }$ less than 2 times of its supplement.
Then, $2({180}^{\circ }-x)-x={60}^{\circ }\Rightarrow {360}^{\circ }-2x-x={60}^{\circ }\Rightarrow {360}^{\circ }-3x={60}^{\circ }\Rightarrow {360}^{\circ }-{60}^{\circ }=3x\Rightarrow {300}^{\circ }=3x\Rightarrow x=\frac{{300}^{\circ }}{3}\Rightarrow x={100}^{\circ }$
If $x={100}^{\circ }$then other angle $={180}^{\circ }-x={180}^{\circ }-{100}^{\circ }={80}^{\circ }$

So, the greater angle is ${100}^{\circ }$.