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

1 Answer
May 14, 2016

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#