Question

Question 10
In the given figure, If $AB||CD,\angle APQ={50}^{\circ }and\angle PRD={130}^{\circ },$ then


(a) ${130}^{\circ }$
(b) ${50}^{\circ }$
(c) ${80}^{\circ }$
(d) ${30}^{\circ }$

Answer 1

Since AB and CD are parallel and PR is a transversal.
$\therefore \angle BPR+\angle PRD={180}^{\circ }$

$\Rightarrow \angle BPR+{130}^{\circ }={180}^{\circ }\Rightarrow \angle BPR={180}^{\circ }-{130}^{\circ }\Rightarrow \angle BPR={50}^{\circ }\Rightarrow {50}^{\circ }+\angle QPR+{50}^{\circ }={180}^{\circ }\Rightarrow \angle QPR+{100}^{\circ }={180}^{\circ }\Rightarrow \angle QPR={180}^{\circ }-{100}^{\circ }\therefore \angle QPR={80}^{\circ }$