Question

angles of a triangle are in ap the greatest angle is doubled the least. find all the angles​

Answer 1

Let the angle A = a

the angle B = a + d

the angle C = a + 2d

It is given that

Angle C = 2 Angle A

a + 2d = 2a

2d = 2a - a

2d = a ... (1)

Now

Angle A + Angle B + Angle C = 180

a + a + d + a + 2d = 180°

3a + 3d = 180°

a + d = 60°

2d + d = 60° ( from (1) )

3d = 60°

d = 20°

Now put value of d in equation 1

a = 2d

a = 2 × 20

a = 40°

the angle A = a = 40°

the angle B = a + d = 40 + 20 = 60°

the angle C = a + 2d = 40 + 40 = 80°

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