Question

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

Answer 1

In a parallelogram, opposite angles are congruent.
$\angle$XYZ = $\angle$XWZ = ${135}^{°}$
Also, WX || ZY
So, $\angle$YZW + $\angle$XWZ = 180$°$ (Since, interior angles on the same side of the transversal are supplementary)
$$\begin{gathered} \Rightarrow \angle \mathrm{YZW}+135°=180° \\ \Rightarrow \angle \mathrm{YZW}=45° \end{gathered}$$
Now l(OY)= 5
we know that diagonals of a parallelogram bisect each other.
So, l(WY) = $2\times \mathrm{OY}=2\times 5=10\mathrm{cm}$