Q. 164.2( 5 Votes )
In an isosceles triangle, the vertex angle is twice the sum of the base angles. Find the angles of the triangle.
Answer :
In a triangle ABC, let ∠A be the vertex angle and ∠C and ∠B be the base angles. It is given that
∠B = ∠C {∵ it is an isosceles triangle}
And ∠A = 2(∠B + ∠C)
⇒ ∠A = 2× 2 ∠B
∠A = 4 ∠B
We know that the sum of the angles of a triangle is 180°.
⇒ 4∠B + ∠B + ∠B = 180°
⇒ 6∠B = 180 °
⇒ ∠B = 30°
So, ∠C = ∠B = 30°
And ∠A = 4× ∠B = 120°
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