Question

In figure, if QT $\perp$ PR, $\angle$TQR = ${40}^{\circ }$, and $\angle$SPR = ${50}^{\circ }$, find the sum of angles x and y.

• A. 110
• B. 120
• C. 130
• D. 150

Answer 1

The correct option is D

150

In $\Delta$TQR, ${90}^{\circ }$ + ${40}^{\circ }$ + $\angle$x = ${180}^{\circ }$ (Angle Sum property)

Therefore $\angle$x = ${50}^{\circ }$

Now $\angle$y = $\angle$SPR + $\angle$x

$\angle$y = ${50}^{\circ }$ + ${50}^{\circ }$ = ${180}^{\circ }$

Now $\angle$x + $\angle$y = ${50}^{\circ }$ + ${100}^{\circ }$ = ${150}^{\circ }$