Question

The angles of a triangle are in AP, and the greatest angle is double the least. Find all the angles in degrees and radians.

Answer 1

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

Since greatest angle is double the least. …………… (given)

So, a + d = 2(a – d)

or a + d = 2a – 2d

or a = 3d ……(1)

Again, by angle sum property, we know

Sum of all the angles = 180 degrees

So, (a – d) + a + (a + d) = 180°

or 3a = 180°

or a = 60° …… (2)

From (1) and (2), we get

3d = 60°

or d = 20°

Now, the angles are,

a – d = 60° – 20° = 40°

a = 60°

a + d = 60° + 20° = 80°.

Therefore the required angles are 40°, 60° and 80°.