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$PQRS$ 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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