Question

If $\angle PQR=\angle PRQ$

then prove that $\angle PQS=\angle PRT$

Answer 1

We are given, $m\angle PQR=m\angle PRQ$..........(1)

Refer image.

Now,

$\angle PQR=\angle PQS$ are linear angles as

$m\angle PQR+m\angle PQS={180}^0$

So, $m\angle PQR=180-m\angle PQS$

Also, $\angle PRQ$ and $\angle PR$ are linear angles as

$m\angle PRQ+m\angle PRT=180$

So, $m\angle PRQ=180-m\angle PRT$

From equation (1),

$180-m\angle PQS=180-\left(m\angle PRT\right)$

$\therefore -\left(m\angle PQS\right)=-\left(m\angle PRT\right)$

$\therefore m\angle PQS=m\angle PRT$