Question

The angles of triangle are in A.P. The greatest angle is twice the least. Find the angles of triangle.

Answer 1

Let a - d, a, a + d be the three angles of the triangle that form AP.

Given that the greatest angle is twice the least.

Now, 2(a - d) = a + d

2a - 2d = a + d

a = 3d ---------------(1)

Now by angle sum property,

(a - d) + a + (a + d) = 180°

3a = 180°

a = 60°----------------------(2)

from (1) and (2),

3d = 60°

d = 20°

Now, the angles are,
a - d = 60°- 20° = 40°
a = 60°
a + d = 60° + 20° = 80°.