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.
• B.
• C.
• D.

Answer 1

The correct option is D

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

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

$\angle$2 = ${70}^{\circ }$

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

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

$\angle$1 = ${45}^{\circ }$

$\angle$1 + $\angle$2 + $\angle$R = ${180}^{\circ }$ (Angle Sum property)

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

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

$\angle$R = ${65}^{\circ }$

$\angle$PRQ = ${65}^{\circ }$
2$\angle$PRQ = ${130}^{\circ }$