Question

The adjacent figure PQRS is a trapezium in which $SP\parallel RQ$, find the measures of $\angle P$ and $\angle R$.

Answer 1

Since PQRS is a trapezium in which $SP\parallel RQ$.

$\therefore \angle P+\angle Q={180}^{\circ }$ and $\angle S+\angle R={180}^{\circ }$

$\Rightarrow \angle P+{130}^{\circ }={180}^{\circ }$ and ${90}^{\circ }+\angle R={180}^{\circ }$

$\Rightarrow \angle P={180}^{\circ }-{130}^{\circ }={50}^{\circ }$ and $\angle R={180}^{\circ }-{90}^{\circ }={90}^{\circ }$