Question

If $ML\parallel NR$, then find the value of y in the following figure.

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${35}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is D ${45}^{\circ }$

If $ML\parallel NR$, then
$\angle APM=\angle PQN$
[Corresponding angles]

Also, $\angle PQN=\angle RQB$, as they are vertically opposite angle.

Therefore, $\angle APM=\angle RQB$.
$\Rightarrow 2y-{30}^{\circ }=3y-{75}^{\circ }\Rightarrow 2y-3y={30}^{\circ }-{75}^{\circ }\Rightarrow -y=-{45}^{\circ }\Rightarrow y={45}^{\circ }$

Hence, the value of y is ${45}^{\circ }$.