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The vertical ∠L of an isosceles ∆LMN is 4 times the ∠M of it.Find ∠N and ∠L.
1. 30 and 120
2. 25 and 100
3. 10 and 40
4. 20 and 80

1 Answer

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Correct Answer - Option 1 : 30 and 120

Given

∠L = 4 × ∠M

Concept

Angel opposite to equal sides of an isosceles triangle are equal

Calculation

Let ∠M = ∠N be x 

So, ∠L = 4x     ----(i)

Since, LM = LN

So, ∠LNM = ∠LMN

⇒ x + 4x + x = 180° 

⇒ 6x = 180°

⇒ x = 30°

So, ∠M = ∠N = 30° 

So, ∠L = 4x = 4 × 30°

⇒ 120°

∴ The value of ∠N and ∠L is 30° and 120°.

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