Question

In the fig, if PQ $\perp$ PS, PQ $\parallel$ SR, $\angle SQR={30}^{\circ },\angle QRT={65}^{\circ }$ then the value of z =${90}^{\circ }$.( Enter 1 if true or 0 otherwise)

Answer 1

Given, $PQ\parallel RT$,
$\angle PQR=\angle QRT$
$\angle PQS+\angle QST=\angle QRT$
$x+30=65$
$x={35}^{\circ }$
In $△PQSS$,
Sum of angles = 180
$\angle PQS+\angle SPQ+\angle PSQ=180$
$35+90+y=180$
$y=180-125$
$y={55}^{\circ }$
Now, $\angle VSQ=\angle SPQ$ (Corresponding angles of parallel lines)
$z=\angle SPQ={90}^{\circ }$