Question

If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle

Answer 1

Let ∠B is the greater angle than by the given condition ∠B = ∠A + ∠C.

Sum of three angles of a triangle = 180°

∠A + ∠B + ∠C = 180°

∠A + (∠A + ∠C) + ∠C = 180°

2∠A + 2∠C = 180°

2(∠A + ∠C) = 180°

∠A + ∠C = `(180^circ)/2`

∠B = 90°

∴ One of the angle of the triangle = 90°

It will be a right angled triangle.