Question

In the fig. given measure of angle $\angle PLN={110}^o$. Then the measure of $\angle LMN$ in degrees is:

Answer 1

In quadrilateral $PLNQ$,
$\angle P+\angle Q+\angle PLN+\angle QNL={360}^o$ ...(By angle sum property, sum of angles of quadrilateral$={360}^o$)
$\therefore {90}^o+{90}^o+{110}^o+\angle QNL={360}^o$
$\therefore \angle QNL={70}^{\circ }$.
In $△LMN$,

$\angle QNL=\angle MNL={70}^o$
$\angle LMN=\angle MNL$ ...(Isosceles triangle property)
$\therefore \angle MNL=\angle LMN={70}^{\circ }$.