Suppose the angles of the triangle be (a – d)°, a° and (a + d)°.
As we know that, the sum of the angles of a triangle is 180°.
a – d + a + a + d = 180°
3a = 180°
a = 60°
Given as
The number of degrees in the least angle/The number of degrees in the mean angle = 1/120
(a - d)/a = 1/120
(60 - d)/60 = 1/120
(60 - d)/1 = 1/2
120 - 2d = 1
2d = 119
d = 119/2
= 59.5
∴ The angles are:
(a – d)° = 60° – 59.5° = 0.5°
a° = 60°
(a + d)° = 60° + 59.5° = 119.5°
The angles of triangle in radians
(0.5 × π/180) rad = π/360
(60 × π/180) rad = π/3
(119.5 × π/180) rad = 239π/360
