A triangle has two corners of angles #pi /6# and #(3pi)/4 #. What are the complement and supplement of the third corner?

1 Answer
Nov 16, 2016

Complement of the third corner is #(5pi)/12# and supplement of the third corner is #(11pi)/12#.

Explanation:

As sum of the angles of a triangle is #pi# and two angles are #pi/6# and #(3pi)/4#, the third angle is given by

#pi-pi/6-(3pi)/4=(12pi-2pi-9pi)/12=pi/12#

As sum of two complementary angles is #pi/2#, complementary angle of third angle is #pi/2-pi/12=(6pi-pi)/12=(5pi)/12#

As sum of two supplementary angles is #pi#, supplementary angle of third ange is #pi-pi/12=(11pi)/12#.