Question

If $x$ and $(20+y{)}^{\circ }$ are the supplementary angles and difference between them is ${60}^{\circ }$, then the value of $y$ is

• A. ${80}^{\circ }$
• B. ${60}^{\circ }$
• C. ${40}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$

$x$ and $(20+y{)}^{\circ }$ are the supplementary angles.
$\therefore x+(20+y{)}^{\circ }={180}^{\circ }\Rightarrow x=(160-y{)}^{\circ }$

Now,
$|(160-y{)}^{\circ }-(20+y{)}^{\circ }|={60}^{\circ }\Rightarrow |{140}^{\circ }-2y|={60}^{\circ }\Rightarrow {140}^{\circ }-2y=\pm {60}^{\circ }\therefore y={100}^{\circ },{40}^{\circ }$