Question

In the given figure, find
$\angle MNR$

Answer 1

$\begin{array}{c}In\Delta QMR\\ {100}^0+{25}^0+\angle Q={180}^0\\ \angle Q={180}^0-{125}^0={55}^0\\ \angle Q=\angle M={55}^0\\ Sumofangles\Delta PNM\\ {55}^0+{55}^0+\angle PNM={180}^0\\ \angle PNM={180}^0-{55}^0-{55}^0={70}^0\end{array}$

PNM is linear pair

$\begin{array}{c}\angle PNM+\angle MQR={180}^0\\ {70}^0+\angle MNR={180}^0\\ \angle MNR={180}^0-{70}^0={110}^0\end{array}$