A triangle has two corners of angles #pi /6# and #(3pi)/8 #. What are the complement and supplement of the third corner?

1 Answer
Oct 29, 2016

Complement of third angle is #pi/24#

and supplement of third angle is #(13pi)/24#

Explanation:

As the two corners of angles are #pi/6# and #(3pi)/8# and sum of angles of a triangle is #pi#

the third angle is #color(white)(XXXX)pi-pi/6-(3pi)/8#

= #(24pi-4pi-9pi)/24=(11pi)/24#

Sum of complementary angle is #pi/2# and sum of supplementary angle is #pi#

Hence complement of third angle, which is #(11pi)/24# is

#pi/2-(11pi)/24=(12pi-11pi)/24=pi/24#

and supplement of third angle is

#pi-(11pi)/24=(24pi-11pi)/24=(13pi)/24#