Question

Diagonals of a parallelogram $WXYZ$ intersect each other at point $O$ . If $\angle XYZ={135}^{\circ }$, then what is the measure $\angle XWZ$ and $\angle YZW$ ?
If $l\left(OY\right)=5cm$ then $l\left(WY\right)=?$

Answer 1

In a parallelogram, diagonal bisect each other

$\therefore OY=OW=5cm$

$\angle XYZ+\angle YZW={180}^{\circ }$ [$\therefore$ interior angles]

${135}^{\circ }+\angle YZW={180}^{\circ }$

$\angle YZW={45}^{\circ }$

In a parallelogram, opposite angles are equal

$\angle XYZ=\angle XWZ={135}^{\circ }$

and OY = 5 cm then WY = OY + OW

$\therefore WY=5+5=10cm$ [opposite diagonal]