91Ó°ÊÓ

The figure is shown below.

Angle sum property of quadrilateral:

$∠1+∠2+∠3+∠4=360°$

Alternate angle property.

Let’s name the points of the triangles as A and B.

In$\mathrm{Δ}WAX$:

To find angle$∠WXA$, substituting the value of angles,

$\begin{array}{c}45+∠WXA+90=180\\ ∠WXA+135=180\end{array}$

Shifting left-hand side value to right-hand side:

$\begin{array}{c}∠WXA=180−135\\ ∠WXA=45\end{array}$

In $\mathrm{Δ}YBZ$:

To find angle$∠BYZ$, substituting the value of angles,

$\begin{array}{c}60+∠BYZ+90=180\\ ∠BYZ+150=180\end{array}$

Shifting left-hand side value to right-hand side:

$\begin{array}{l}∠BYZ=180−150\\ ∠BYZ=30\end{array}$

Considering the alternate angle property, which states that when the lines are parallel, that the alternate interior angles are equal. Hence,

$∠XAW=∠YXA$,

$∠YXA=90$, and

$∠ZBY=∠XYB$

$∠XYB=90$

For$∠WXY$,

$\begin{array}{c}∠WXY=∠YXA+∠WXA\\ ∠WXY=45+90\\ ∠WXY=135\end{array}$

For$∠XYZ$,

$\begin{array}{c}∠XYZ=∠XYB+∠ZYB\\ ∠XYZ=30+90\\ ∠WXY=120\end{array}$

Hence,

$\begin{array}{c}∠WXY=135°\\ ∠XYZ=120°\end{array}$