Question

In figure, if QT is perpendicular to PR, $\angle TQR={40}^{\circ }$ and $\angle SPR={30}^{\circ }$ , find x and y.

Answer 1

In $\Delta TQR$,

$\angle TQR+\angle QTR+\angle QRT={180}^{\circ }$

$\Rightarrow {40}^{\circ }+{90}^{\circ }+x={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-{130}^{\circ }$

$\Rightarrow x={50}^{\circ }$

In $\Delta PSR$

$y=x+{30}^{\circ }$ (Sum of interior opposite angles is equal to to exterior angle)

$\Rightarrow y={50}^{\circ }+{30}^{\circ }$

$\Rightarrow y={80}^{\circ }$​

Hence, $x={50}^{\circ },y={80}^{\circ }$​