In an isosceles triangle, if the vertex angle is twice the

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In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of the half of the vertex angle of the triangle is

1. 60°
2. 70°
3. 80°
4. 50°

Correct Option: A

On the basis of given in question , we draw a figure of an isosceles triangle ABC ,

In ∆ ABC,
AB = AC
∴ ∠ABC = ∠ACB = y°
∴ ∠BAC = 4y
As we know that , ∠A + ∠B + ∠C = 180°
∴ 4y + y + y = 180°
⇒ 6y = 180°
⇒ y = 30°
∴ ∠BAC = 4 × 30° = 120°

∠BAD =	1	∠BAD = 60°
	2