Question

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Answer 1

Given that, the angles of a triangle are in AP.

Let A, B and C are angles of a ∆ABC

B = `(A + C)/2`

⇒ 2B = A + C  ...(i)

We know that, sum of all interior angles of a ∆ABC is 180°

A + B + C = 180°

⇒ 2B + B = 180°  ...[From equation (i)]

⇒ 3B = 180°

⇒ B = 60°

Let the greatest and least angles are A and C respectively

A = 2C [by condition]  ...(ii)

Now, put the values of B and A in equation (i), we get

2 × 60° = 2C + C

⇒ 120° = 3C

⇒ C = 40°

Put the value of C in equation (ii), we get

A = 2 × 40°

⇒ A = 80°

Hence, the required angles of a triangle are 80°, 60° and 40°.