Question

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

Options

• obtuse

• acute

• right

• equilateral

Answer 1

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

Explanation:

Let A, B and C be the angles of the triangle.

Then, one angle of a triangle is equal to the sum of the other two angles,

i.e. ∠A = ∠B + ∠C  ...(i)

As we know, ∠A = ∠B + ∠C = 180°  ...[Angle sum property of a triangle]

⇒ ∠A + ∠A = 180°  ...[From equation (i)]

⇒ 2∠A = 180°

⇒ ∠A = `180^circ/2`

⇒ ∠A = 90°

Hence, the triangle is right-angled.