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

1 Answer
Dec 27, 2016

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#.