$PQRS$ is a trapezium in which $PQ||SR$ and $\angle P=130^{\circ}, \angle Q=110^{\circ}$. Then find $\angle R$ and $\angle S$.

Given: $PQRS$ is a trapezium in which $PQ||SR$ and $\angle P=130^{\circ}, \angle Q=110^{\circ}$.

To do: To find $\angle R$ and $\angle S$.

Solution:

 In trapezium $PQRS$, adjacent angles are supplementary

$\Rightarrow P+S=180^o$                               

$\Rightarrow 130^o+S=180^o$

$\Rightarrow S=180^o-130^o=50^o$

Similarly $\angle Q$ and $\angle R$ are also adjacent angles.

$\Rightarrow Q+R=180^o$

$\Rightarrow 110^o+R=180^o$

$\Rightarrow R=180^o-110^o=70^o$

Thus, $\angle R=70^o$ and $\angle S=50^o$.

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Updated on: 10-Oct-2022

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