Question

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

विकल्प

•  100°

•  120°

•  110°

•  130°

Answer 1

Let ABCbe isosceles triangle 

Then

AB = AC 

∠B = ∠C

Now it is given that vertex angle is 2 times the sum of base angles 

⇒∠A = 2 ∠(B+ C)

⇒∠A = 2 ∠(∠B + ∠B ) (As ∠B = ∠C)

⇒∠A = 2 (2∠B)

⇒∠A = 4 ∠B

Now 

∠A + ∠B + ∠C = 180° (Property of triangle)

 4∠B + ∠B + ∠B = 180° (Since ∠A = 4∠B, and ∠B = ∠C )

6∠B = 180°

∠B = 30° 

∠A = 4∠B

 `= 4 xx 30°`

 = 120°