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 = \(77^\circ\)