Question

In figure, if $PQ\perp PS,PQ\parallel SR,\angle SQR={28}^o$ and $\angle QRT={65}^o$, then find the value of x and y.

• A. $x={37}^o$
• B. $x={53}^o$
• C. $y={37}^o$
• D. $y={53}^o$

Answer 1

Answer: (A), (D)

The correct options are
A $x={37}^o$
D $y={53}^o$

$\angle QSR=x$ (alternate angles)

Now, $\angle QSR+{28}^o$ =${65}^o$

$x+{28}^o$ = ${65}^o$

$x={37}^o$

In PQS,${90}^o+x+y={180}^o$

${90}^o$ + ${37}^o+y={180}^o$

$y={53}^o$