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 in degrees.

• A. 130

Answer 1

The correct option is A 130
${110}^{\circ }$ + $\angle$2 = ${180}^{\circ }$ (by linear pair)

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

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

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

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

$\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 = ${130}^{\circ }$