Question

A triangle has two corners of angles `pi /8` and `(pi)/3`. What are the complement and supplement of the third corner?

Answer 1

Complement: `(-pi/24)` ... but see Note 1 below.

Supplement: `(11pi)/24`

Explanation:

The complement of any angle `theta` is `pi/2-theta`.

The supplement of any angle `theta` is `pi-theta`.

The Sum of the Interior Angles of a Triangle is `pi`.

If two of the interior angles of a triangle are `pi/8` and `pi/3`
then the third interior angle is `pi-(pi/8+pi/3)=pi-(11pi)/24= (13pi)/24`

The complement of this third angle is `pi/2-(13pi)/24=-pi/24`
`color(white)("XXX")`Note 1: some people will claim that there is no
`color(white)("XXX")`complement for an angle which is greater than `pi/2`;
`color(white)("XXX")`check with your instructor.

The supplement of this third angle is `pi-(13pi)/24=(11pi)/24`.
`color(white)("XXX")`Note 2: the supplement of the third angle of a
`color(white)("XXX")`triangle will always be the sum of the other two
`color(white)("XXX")`angles.