The angles of a triangle are in AP and the ratio of the number of degrees in the least to the number of radians in the greatest is 60: π. Find the angles in degrees and radians.

Let the angles of the triangle be  (a – d)°,  a°  and  (a + d)°.  Then,

(a – d) + a + (a + d) = 180°

⇒  3a = 180°

⇒  a = 60°

So,  the angles are (60 – d)°, 60°, (60 + d)°.

It is clear that,  (60 – d)°  is the least angle and  (60 + d)°  is the greatest angle.

Now, greater angle  =  (60 + d)°  =  

It is given that,

Hence, the angles are (60 – 30)°, 60°, (60 + 30)°  i.e., 30°, 60°, 90°.