Question

A triangle has two corners of angles `(3pi )/8` and `(pi)/4`. What are the complement and supplement of the third corner?

Answer 1

Complementary angle of `color(indigo)(hat C = pi/4`

Supplementary angle of `color(crimson)(hat C = (5pi)/8`

Explanation:

Sum of the angles of a triangle is `pi^c or 180^@`

`hat A + hat B + hat C = 180^@ or pi^c`

`hat C = pi - (3pi)/8 - pi/4 = (3pi)/8`

Complementary angle of `hat C = pi/2 - (3pi)/8 = pi/4`

Supplementary angle of `hat C = pi - (3pi)/8 = (5pi)/8`