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

$As,{110}^{\circ }+\angle 2={180}^{\circ }$ [Linear pair]

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

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

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

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