In the given figure, if $P Q \perp P S, P Q \| S R, \angle S Q R=28^{\circ}$ and $\angle Q R T=65^{\circ}$, then find the values of $x$ and $y$.


It is given that $P Q \| S R$ and $Q R$ is a transversal line.

$\angle P Q R=\angle Q R T$ (Alternate interior angles)




By using the angle sum property for $\triangle S P Q$, we obtain

$\angle S P Q+x+y=180^{\circ}$




$\therefore x=37^{\circ}$ and $y=53^{\circ}$

Leave a comment