Question

A triangle has two corners of angles `(3pi )/8` and `(5pi)/12`. What are the complement and supplement of the third corner?

Answer 1

Complementary angle is `(7pi)/24` and supplementary angle is `(19pi)/24`

Explanation:

The two angles of the triangle are `(3pi)/8` and `(5pi)/12`.

As sum of angles of a triangle is `pi`, the third angle is

`pi-(3pi)/8-(5pi)/12=(24pi)/24-(9pi)/24-(10pi)/24=(5pi)/24`

Now complementary angles add up to `pi/2` and supplementary angles add up to `pi`.

Hence complementary angle of third angle `(5pi)/24` is `pi/2-(5pi)/24=(12pi)/24-(5pi)/24=(7pi)/24`

and supplementary angle of third angle `(5pi)/24` is `pi-(5pi)/24=(24pi)/24-(5pi)/24=(19pi)/12`