If the sum of two angles is `135^(@)` and their difference is `(pi)/(12)`, then determine the sexagesimal value and circular value of two angles .

Explanation

Let the two angles be `x^(@)` and `y^(@) (x gt y)`.
As per question, `x+y = 135`……………`(i)`
and `x-y = (pi)/(12) = (180)/(12) = 15`………………..(2)
Now, adding (1) and (2) we get, `2x =150`
or, `x=(150)/(2) = 75 = 75xx(pi)/(180) = (5pi)/(12`
From (1) we get, `75+y =135` or, `y-135 - 75 or , y = 60. = 60xx(pi)/(180) = (pi)/(3)`
Hence the sexagesimal values of the angles are `75^(@) and 60^(@)` and the circular values are `(5pi)/(12) and (pi)/(3)`.