Question

What is the complimentary and supplementary angle to `(2pi)/7`?

Answer 1

Complimentary angles are those which add up to `pi/2`.
Let `theta` be the complimentary angle to `(2pi)/7`, then by definition
`theta+(2pi)/7=pi/2`
`implies theta=pi/2-(2pi)/7=(7pi-4pi)/14=(3pi)/14`
Therefore, the complimentary angle to `(2pi)/7`is `(3pi)/14`.

Supplementary angles re those which add up to `pi`.
Let `phi` be the supplementary angle to `(2pi)/7`, then by definition
`phi+(2pi)/7=pi`
`implies phi=pi-(2pi)/7=(7pi-2pi)/7=(5pi)/7`
Therefore, the complimentary angle to `(2pi)/7`is `(5pi)/7`.