Question

WXYZ is a parallelogram. Find the angle XYP (in degrees).

• A. 135

Answer 1

The correct option is A 135

$\text{Given}\angle W={45}^{\circ }$

$\text{We know,}\angle \text{W and}\angle \text{Z are co-interior angle pairs.}$

$\therefore \angle W+\angle Z={180}^{\circ }$

$\Rightarrow {45}^{\circ }+\angle Z={180}^{\circ }$

$\Rightarrow \angle Z={180}^{\circ }-{45}^{\circ }$

$\Rightarrow \angle Z={135}^{\circ }$

$\text{We know,}\angle \text{Z and}\angle \text{Y are adjacent angles}$

$\therefore \angle Z+\angle Y={180}^{\circ }$

$\Rightarrow \angle Y={180}^{\circ }-{135}^{\circ }$

$\Rightarrow \angle Y={45}^{\circ }$

$\text{We know,}\angle \text{Y and}\angle \text{XYP are adjacent angles}$

$\therefore \angle Y+\angle XYP={180}^{\circ }$

$\Rightarrow \angle XYP={180}^{\circ }-{45}^{\circ }$

$\Rightarrow \angle XYP={135}^{\circ }$

$\text{Therefore, the value of}\angle XYP\text{is}{135}^{\circ }.$