Question

In the given figure, LM = LN and $\angle PLN={110}^{\circ }$. Find $\angle LMN$.

• A. $\angle LMN={70}^{\circ }$
• B. $\angle LMN={60}^{\circ }$
• C. $\angle LMN={50}^{\circ }$
• D. $\angle LMN={40}^{\circ }$

Answer 1

The correct option is A $\angle LMN={70}^{\circ }$



In quad. PQNL,
$\angle QPL+\angle PLN+\angle LNQ+\angle NQP={360}^{\circ }$
${90}^{\circ }+{110}^{\circ }+\angle LNQ+{90}^{\circ }={360}^{\circ }$
$\angle LNQ={360}^{\circ }-{290}^{\circ }$
$\angle LNQ={70}^{\circ }$
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In triangle LMN,
$LM=LN$ [Given]
[Angles opposite to equal sides are equal]
$\angle LMN=\angle LNM$ [$\angle LNQ=\angle LMN$]
$\angle LMN={70}^{\circ }$
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