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