Question

$PQRS$ is a trapezium with $PQ\parallel SR$. $\angle P={30}^o$ $\angle Q={50}^o$, find $\angle R$ and $\angle S$

Answer 1

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Since PQ||SR, and PS is transversal then

$\angle P+\angle S={180}^{\circ }$ (sum of consecutive interior angles on the same of transversal is ${180}^{\circ }$)

${30}^{\circ }+\angle S={180}^{\circ }$

$\angle S={180}^{\circ }-{30}^{\circ }$

$\angle S={150}^{\circ }$

Since PQ||SR , and QR is transversal then

$\angle Q+\angle R={180}^{\circ }$ (sum of consecutive interior angles on the same side of transversal is ${180}^{\circ }$)

${50}^{\circ }+\angle R={180}^{\circ }$

$\angle R={180}^{\circ }-{50}^{\circ }$

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