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

Let A, B and C be the three angles in AP (in degrees)

And A being the least and C being the greatest

Then

C = 2A [ Given][ eqn i]

B - A = C - B

2B = A + C

2B = A + 2A [ using eqn i]

2B = 3A

B = 3A/2 [ eqn ii]

Using the angle sum property of triangle

A + B + C = 180°

9A = 360

A = 40°

B = 3(40)/2 = 60° [ using ii]

C = 2(40) = 80° [ using i]