In the given figure- LM - LN and - P LN -110- Find - LMN-A- 70

The correct option is A 70In quad. PQNL, ∠ QPL +∠ PLN +∠ LNQ + ∠ NQP = 360^∘ 90^∘ +110^∘ +∠ LNQ + 90^∘ = 360^∘ ∠ LNQ nbsp; = 360^∘ 290^∘ ∠ LNQ = 70^∘ In ...

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Standard IX

Mathematics

Isosceles Triangle

In the given ...

Question

In the given figure, LM = LN and $∠ P L N = 110^{\circ}$ . Find $∠ L M N$ .
70

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Solution

The correct option is A 70
In quad. PQNL,
$∠ Q P L + ∠ P L N + ∠ L N Q + ∠ N Q P = 360^{\circ}$
$90^{\circ} + 110^{\circ} + ∠ L N Q + 90^{\circ} = 360^{\circ}$
$∠ L N Q = 360^{\circ} - 290^{\circ}$
$∠ L N Q = 70^{\circ}$

In triangle LMN,
$L M = L N$ [Given]
[Angles opposite to equal sides are equal]
$∠ L M N = ∠ L N M$ [ $∠ L N Q = ∠ L M N$ ]
$∠ L M N = 70^{\circ}$

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In the given figure, LM = LN and ∠PLN=110∘. Find ∠LMN.70

The correct option is A 70In quad. PQNL, ∠QPL+∠PLN+∠LNQ+∠NQP=360∘ 90∘+110∘+∠LNQ+90∘=360∘ ∠LNQ=360∘−290∘ ∠LNQ=70∘ ​​​ In triangle LMN, LM=LN [Given] [Angles opposite to equal sides are equal] ∠LMN=∠LNM [∠LNQ=∠LMN] ∠LMN=70∘ ​​​​

In the given figure, LM = LN and $∠ P L N = 110^{\circ}$ . Find $∠ L M N$ .
70