Question

A triangle has two corners of angles `(pi )/6` and `(7pi)/12`. What are the complement and supplement of the third corner?

Answer 1

Complement: `pi/4color(white)("XXXXXX")`Supplement: `(3pi)/4`

Explanation:

If two angles of a triangle are `pi/6` and `(7pi)/12`
the third angle must be
`color(white)("XXX")pi-(pi/6+(7pi)/12)=pi-(9pi)/12=pi/4`

Complementary angles add up to `pi/2`
so the complement of the third angle must be `pi/2-pi/4=pi/4`

Supplementary angles add up to `pi`
so the supplement of the third angle must be `pi=pi/4=(3pi)/4`