Question

A triangle has two corners of angles `pi /12` and `(3pi)/8`. What are the complement and supplement of the third corner?

Answer 1

As the third angle is greater than `pi/2`, there is no complementary angle of the third angle. Supplementary angle is `(11pi)/24`

Explanation:

Three facts are required to solve this.

(1) Sum of interior angles of a triangle is `180^@` or `pi`. As two angles of a triangle are `pi/12` and `(3pi)/8`, the third angle is `pi-pi/12-(3pi)/8=(24pi)/24-(2pi)/24-(9pi)/24=(13pi)/24`.

(2) Sum of the complementary angles is `pi/2`. But as third angle is `(13pi)/24` and is greater than `pi/2=(12pi)/24`, there cannot be a complementary angle of the third angle.

(3) Sum of the supplementary angles is `pi`. As third angle is `(13pi)/24` its supplementary angle is `pi-(13pi)/24=(24pi)/24-(13pi)/24=(11pi)/24`.