Question

In the figure, $LM=LN,\angle PLN={110}^{\circ }$. Then,the measure of $\angle MLN$ in degrees is____.

• A. ${110}^{\circ }$
• B. ${40}^{\circ }$
• C. ${10}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

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

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

We know, sum of angles of the $△LMN$,
$\angle MLN+\angle LNM+\angle LMN={180}^o$
$\angle MLN+{70}^o+{70}^o={180}^o$
$\angle MLN={180}^o-{140}^o$
$\angle MLN={40}^{\circ }$.

Therefore, option $B$ is correct.