Question

In the given figure, LM = LN; angle PLN $={110}^{\circ }$. Calculate :$\angle MLN$

• A. ${32}^o$
• B. ${42}^o$
• C. ${40}^o$
• D. ${50}^o$

Answer 1

The correct option is C ${40}^o$

Given, $\angle P=\angle Q={90}^{\circ }$ and $\angle PLN={110}^{\circ }$
In quadrilateral PLNQ,
$\angle P+\angle Q+\angle PLN+\angle LNQ={360}^{\circ }$
${90}^{\circ }+{90}^{\circ }+{110}^{\circ }+\angle LNQ={360}^{\circ }$
$\angle LNQ={70}^{\circ }$
In $△LMN$, given LM = LN thus, $\angle LNQ=\angle LMN={70}^{\circ }$
As, $\angle LNQ+\angle LMN+\angle MLN={180}^{\circ }$
${70}^{\circ }+{70}^{\circ }+\angle MLN={180}^{\circ }$
$\angle MLN={40}^{\circ }$