Question

the angles of triangles are in AP and the number of degree in the list is to be number of Radians in the greatest as 60 to π, find the angles in degrees

Answer 1

Let the angles of the triangle are (a - d), a, (a + d)

Now, in a triangle, the sum of all angles equal to 180 degree

=> (a - d) + a + (a + d) = 180

=> a - d + a + a + d = 180

=> 3a = 180

=> a = 180/3

=> a = 60

Now, the angle are (60 - d), 60, (60 + d)

Now, 60 - d is the least and 60 + d is the greatest angle.

Now, (60 + d)° = {(60 + d) * (π/180)}c

Given that, number of radians in the greatest angle/number of degrees in the least one = π/60

=> {(60 + d) * (π/180)}c /(60 - d) = π/60

=> (60 - d)/{(60 + d) * (π/180)}c = 60/π

=> 180(60 - d)/{(60 + d) * π} = 60/π

=> 180(60 - d)/(60 + d) = 60

=> (60 - d)/(60 + d) = 60/180

=> (60 - d)/(60 + d) = 1/3

=> 3(60 - d) = (60 + d)

=> 180 - 3d = 60 + d

=> 180 - 60 = 3d + d

=> 4d = 120

=> d = 120/4

=> d = 30

Now, the angles are (60 - 30), 60, (60 + 30) = 30, 60, 90