Question

in an isosceles triangle, if the vertex angle is twice the sum of base angles, calculate the angle of a traingle

Answer 1

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Answer 2

Given that,

An isosceles triangle.

To find,

If the vertex angle is twice the sum of base angles, calculate the angle of a triangle.

Solution,

Let ABC is an isosceles triangle with AB = BC.

⇒ ∠B=∠C

According to question,

The vertex angle is twice the sum of base angles, it means,

∠A=2(∠B+∠C)

∠A=2(∠B+∠B) (given)

∠A=4∠B

Sum of angles of a triangle is equal to 180°

So,

∠A+∠B+∠C=180

4∠B+∠B+∠B=180

6∠B=180

∠B=30°

So, ∠C=∠B=30°

And

∠A=4∠B

∠A=4×30

∠A=120°

So, angles are 30°, 30° and 120°