Question

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

• A. ${62}^o$
• B. ${72}^o$
• C. ${70}^o$
• D. none of the above

Answer 1

The correct option is C ${70}^o$

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, $\angle LNQ=\angle LMN={70}^{\circ }$