A triangle has two corners of angles #pi /8# and #(2pi)/3 #. What are the complement and supplement of the third corner?

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Answer 1 · 2016-07-26T11:25:52

The supplement of the third corner angle#=19pi/24#.

The complement of the third corner#=7pi/24#.

The sum of corner angles of a triangle is #pi#.

We are given two corner angles #pi/8 and, 2pi/3#.

Therefore, the third corner angle #=pi-(pi/8+2pi/3)=pi-19pi/24#.

Hence, the supplement of the third corner angle#=pi-(pi-19pi/24)=19pi/24#.

The complement of the third corner#=pi/2-(pi-19pi/24)#
#=19pi/24+pi/2--pi=(19pi+12pi-24pi)/24=7pi/24#.