Question

In the figure, $PQRS$ is an isosceles trapezium; $\angle SRP={30}^{\circ }$, and $\angle PQS={40}^{\circ }$. Calculate the angles $\angle RPQ$ and $\angle RSQ$

Answer 1

Given that: $PQRS$ is an isosceles trapezium,
Hence, $PS=RQ$
$\angle SRP$ $={30}^{\circ }$ and $\angle PQS$ $={40}^{\circ }$
To find: $\angle RPQ$ and $\angle RSQ$
$\angle RPQ$ $=\angle SRP$ $={30}^{\circ }$
(Alternate angles, $PQ\parallel SR$)
$\angle RSQ$ $=\angle PQS$ $={40}^{\circ }$
(Alternate angles, $PQ\parallel SR$)