Question

4. In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

​

Answer 1

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°.

hope it helps ❣️ ❣️