Question

In the figure, sides QP and RQ of $\Delta$PQR are produced to points S and T, respectively. If $\angle$SPR = ${135}^{\circ }$ and $\angle$PQT = ${110}^{\circ }$, find 2$\angle$PRQ.

• A. ${90}^{\circ }$
• B. ${150}^{\circ }$
• C. ${110}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is D

${130}^{\circ }$

As, ${110}^{\circ }$ + $\angle$2 = ${180}^{\circ }$ ($\because$ linear pair)

So, $\angle$2 = ${180}^{\circ }$ – ${110}^{\circ }$

i.e, $\angle$2 = ${70}^{\circ }$

Also, $\angle$1 + ${135}^{\circ }$ = ${180}^{\circ }$ ($\because$ linear pair)

$\angle$1 = ${180}^{\circ }$ – ${135}^{\circ }$

i.e, $\angle$1 = ${45}^{\circ }$

Also, $\angle$1 + $\angle$2 + $\angle$R = ${180}^{\circ }$ (angle sum property)

Or, ${45}^{\circ }$ + ${70}^{\circ }$ + $\angle$R = ${180}^{\circ }$

$\angle$R = ${180}^{\circ }$ – ${115}^{\circ }$

i.e, $\angle$R = ${65}^{\circ }$

Therefore, 2$\angle$PRQ = ${130}^{\circ }$