Question

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ______.

Options

• an isosceles triangle

• an obtuse triangle

• an equilateral triangle

• a right triangle

Answer 1

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle.

Explanation:

Given, Let angle of triangle ABC be ∠A, ∠B and ∠C

Given that: ∠A = ∠B + ∠C  ...(i)

We know that in any triangle ∠A + ∠B + ∠C = 180°  ...(ii)

From equation (i) and (ii), get:

∠A + ∠A = 180°

2∠A = 180°

`∠A = (180^circ)/2`

∠A = 90°

Hence, the triangle is a right triangle.