In the given figure, if $A B \| C D, \angle A P Q=50^{\circ}$ and $\angle P R D=127^{\circ}$, find $x$ and $y$.


$\angle \mathrm{APR}=\angle \mathrm{PRD}$ (Alternate interior angles)




Also, $\angle \mathrm{APQ}=\angle \mathrm{PQR}$ (Alternate interior angles)


$\therefore x=50^{\circ}$ and $y=77^{\circ}$

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