Question

In figure if $QT\perp PR,\angle TQR={40}^{\circ }$ and $\angle SPR={30}^{\circ },$ find the vlaues of $x$ and $y$.

Answer 1

Consider $QTR$

$TQR+QTR+R={180}^o$

(Sum of angle of a triangle in ${180}^o$)

${40}^o+{90}^o+R={180}^o$

$R={50}^o$

Now ,Consider $PRS$

$y=SPR+x$

(Exterior angle is equal to sum of interior angles)

$y={30}^o+{50}^o$

$={80}^o$

Hence, $x={50}^o,y={80}^o$