Question

In the given figure, line PQ and line MN intersect at O. Determine the value of $y$ when $x=60°$. Further, determine the value of $x$ when $y=40°$.

• A. $y=60°$ and $x=70°$
• B. $y=70°$ and $x=60°$
• C. $y=50°$ and $x=80°$
• D. $y=80°$ and $x=50°$

Answer 1

The correct option is A $y=60°$ and $x=70°$

From the given figure, $\angle POM$ and $\angle MOQ$ form a linear pair of angles.
$\Rightarrow 2x+y={180}^{\circ }$

Case (1) : When $x={60}^{\circ }$
$2\times {60}^{\circ }+y={180}^{\circ }$
$\Rightarrow y={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

Case (2) : When $y={40}^{\circ }$
$2x+{40}^{\circ }={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-{40}^{\circ }={140}^{\circ }$
$\Rightarrow x={70}^{\circ }$
$\therefore$ When $x={60}^{\circ }$, $y={60}^{\circ }$ and when $y={40}^{\circ }$, $x={70}^{\circ }$.