Question

Question 21

If two supplementary angles are in the ratio 1: 2 , then bigger angle is
(a) ${120}^{\circ }$
(b) ${125}^{\circ }$
(c) ${110}^{circ}$
(d) ${90}^{\circ }$

Answer 1

It is given that the angle are in the ratio of 1:2 let the angles wil be x and 2x Also, the two angles are supplementary i.e. their sum is equal to ${180}^{\circ }$.
$\therefore x+2x={180}^{\circ }\Rightarrow 3x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{3}\Rightarrow x={60}^{\circ }$

Hence the required angles are ${60}^{\circ }$ and $2\times {60}^{\circ },i.e.{60}^{\circ }and{120}^{\circ }$.

Bigger of the two angles is ${120}^{\circ }$.