Question

In figure given $\angle PQR=\angle PRQ,$ , then prove that $\angle PQS=\angle PRT$.

Answer 1

We have,

Given that, $\angle PQR=\angle PRQ$

Let $\angle PQR=x$ then $\angle PRQ=x$

Now, we know that

$\angle PQS+\angle PQR={180}^o$

$\angle PQS={180}^o-\angle PQR$

$\angle PQS={180}^o-x.......\left(1\right)$

Also, we can say that,

$\angle PRT+\angle PRQ={180}^o$

$\angle PRT={180}^o-\angle PRQ$

$\angle PRT={180}^o-x......\left(2\right)$

By equation (01 and (2) to and we get,

$\angle PQS=\angle PRT$

Hence proved.