Question

$PQRS$ is a trapezium in which $SP||RQ$, find the measures of $\angle P$ and $\angle R$. Give reasons.

Answer 1

$\Rightarrow$ $PQRS$ is trapezium.

$\Rightarrow$ $SP\parallel RQ$ [ Given ]

We know, sum of two angles between parallel lines is supplementary

$\therefore$ $\angle QRS+\angle RSP={180}^o$

$\Rightarrow$ $\angle QRS+{90}^o={180}^o$

$\Rightarrow$ $\angle QRS={180}^o-{90}^o={90}^o$

$\Rightarrow$ $\angle PQR+\angle QRS+\angle RSP+\angle SPQ={360}^o$

$\Rightarrow$ ${100}^o+{90}^o+{90}^o+\angle SPQ={360}^o$

$\Rightarrow$ ${280}^o+\angle SPQ={360}^o$

$\Rightarrow$ $\angle SPQ={360}^o-{280}^o={80}^o$

$\therefore$ Measures of $\angle P$ and $\angle R$ are ${80}^o$ and ${90}^o$