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# In figure, if AB || CD, $$\angle{APQ}$$ = $$50^\circ$$ and $$\angle{PRD}$$ = $$127^\circ$$, find x and y.

We have, AB || CD

$$\angle{PQR}$$ = $$\angle{APQ}$$ ....(Alternate interior angles)

$$\therefore$$ x = $$50^\circ$$ ....(i)(given, $$\angle{APQ}$$ = $$50^\circ$$))

Now, as we know that, Exterior angle is equal to sum of interior opposite angles of a triangle.
$$\therefore$$ (\angle{PQR}\) + $$\angle{QPR}$$ = $$127^\circ$$
from (i), we get,

$$\because$$ $$50^\circ$$ + $$\angle{QPR}$$ = $$127^\circ$$
$$\Rightarrow$$ y = $$77^\circ$$