Question

Question 5
In the given figure, if $PQ\perp PS,PQ||SR,\angle SQR={28}^{\circ }$ and $\angle QRT={65}^{\circ }$, then find the values of x and y.

Answer 1

It is given that $PQ||SR$ and $QR$ is a transversal line.
$\angle PQR=\angle QRT$ (Alternate interior angles)
$x+{28}^{\circ }={65}^{\circ }$
$x={65}^{\circ }-{28}^{\circ }$
$x={37}^{\circ }$
By using the angle sum property for $△SPQ,$ we obtain,
$\angle SPQ+x+y={180}^{\circ }$
${90}^{\circ }+{37}^{\circ }+y={180}^{\circ }$
$y={180}^{\circ }-{127}^{\circ }$
$y={53}^{\circ }$
$\therefore x={37}^{\circ }andy={53}^{\circ }$