The angles of a triangle are in A. P. and the number of degrees in the least angles is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians .

Given that angles are in AP, Let the three angles be,

(a – d), a and (a + d)

Such that, all three angles are in degrees and d>0 such that (a – d) is the least angle.

We know, By triangle sum property

(a – d) + a + (a + d) = 180

⇒ 3a = 180

⇒ a = 60°

Also given, the number of degrees in the least angle is to the number of degrees in the mean angle is 1:120

Least angle = (a – d)

⇒ 60 – d = 0.5

⇒ d = 59.5

Hence, angles are

(a – d) = 60 – 59.5 = 0.5°

a = 60°

(a + d) = 60 + 59.5 = 119.5°

Now, If θ is the angle in degree than the angle in radians is equal to

Hence, angles in radians are

Angle 1:

Angle 2:

Angle 3: