Question

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

Answer 1

$\text{Given}\angle XYZ={135}^{\circ }$
Opposite angles of a parallelogram are congruent.
$\angle XWZ=\angle XYZ={135}^{\circ }$
Adjacent angles of a parallelogram are supplementary.
$\angle YZW+\angle XWZ={180}^{\circ }$
$\angle YZW+{135}^{\circ }={180}^{\circ }$
$\angle YZW={180}^{\circ }-{135}^{\circ }={45}^{\circ }$
$\text{Given}l\left(OY\right)=5\text{cm}$
Diagonals of a parallelogram bisect each other.
$l\left(WY\right)=2\times OY=2\times 5=10\text{cm}$
Measure of $\angle XWZand\angle YZWare{135}^{\circ }\text{and}{45}^{\circ }$ respectively.
Length of WY is 10 cm.