Question

In the given figure, if MN and PQ are parallel, find the value of (∠X + ∠Y).

• A. 30°
• B. 105°
• C. 130°
• D. 105°

Answer 1

The correct option is B 105°

MN and PQ are parallel lines and PN is transversal.
$\therefore \angle QPN=\angle MNP$
[Alternate interior angles]

$\text{So,}\angle QPN=\text{X}={30}^{\circ }$

$\text{Now,}\angle \text{Y}=\angle PQM+\angle QPN$
[Exterior angle property]

$\Rightarrow \angle \text{Y}={45}^{\circ }+{30}^{\circ }\Rightarrow \angle \text{Y}={75}^{\circ }$

$\text{So, value of}\angle \text{X +}\angle \text{Y}={30}^{\circ }+{75}^{\circ }={105}^{\circ }$