Question

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

Answer 1

complement: `0`
supplement: `pi/2 = 90^@`

Explanation:

Two angles are complementary if the add up to `pi/2 = 90^@`.
Two angles are supplementary if they add up to `pi = 180^@`

Since the interior angles of a triangle add up to `pi=180^@`
if two angles of a triangle are `pi/8` and `(3pi)/8`
then the third angle will be
`color(white)("XXX")pi - (pi/8+(3pi)/8) = pi/2=90^@`

and
`color(white)("XXX")`the complement of this third angle will be `0`
and
`color(white)("XXX")`the supplement of this third angle will be `pi/2=90^@`