Question

If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?

Answer 1

`pi / 12 " rad"`

Explanation:

Let's try to write down what is being stated.

Let `theta` be the angle.
(7 times the complement of the angle) - (3 times the supplement of an angle) = one third of a right angle.
`=> 7 ( pi / 2 - theta ) - 3 ( pi - theta ) = ( pi / 2 ) / 3 = pi / 6`
`=> ( 7 pi ) / 2 - 7 theta - 3 pi + 3 theta = pi / 6`
`=> 4 theta = pi / 2 - pi / 6 = pi / 3`
`=> theta = pi / 12`.

Remark :
Replace `pi " radians"` by `180 " degrees"` and continue the computation in the same way if you are more comfortable with degrees.