Question

In the given figure, if MN and PQ are parallel, find the value of $\text{X}+\text{Y}$ in degrees.

• A. 105

Answer 1

The correct option is A 105
MN and PQ are parallel lines and PN is transversal.
$\angle QPN=\angle MNP$
[Alternate interior angles are equal]
$\angle QPN=\text{X}={30}^{\circ }$
$\text{Y}=\angle PQM+\angle QPN$ [Exterior angle property]
$\text{Y}={45}^{\circ }+{30}^{\circ }\text{Y}={75}^{\circ }$
$\text{X}+\text{Y}$ = ${30}^{\circ }+{75}^{\circ }$ = ${105}^{\circ }$