The sum of two angles is 5π c and their difference is 60° find the measures in degree

We know that, 1c = `(180/pi)^circ`

∴ 5πc = `(5pi xx 180/pi)^"c"` = 900°

Let the degree measures of the angles be x and y.

Then x + y = 900°  ...(1)

and x – y = 60°  ...(2)

2x = 960°

x = 480°

Adding (1) and (2), we get,

2x = 960°  ∴ x = 480°

∴ Substituting the value of x in (1), we get480° + y = 900°

∴ y = 900° − 480°

∴ y = 420°

Hence, the degree measures of the two angles are 480° and 420°.