A triangle has two corners of angles #pi /12# and #(7pi)/12 #. What are the complement and supplement of the third corner?

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Answer 1 · 2017-11-09T17:39:43

The complement is #pi/6#radians.

The supplement is #(2pi)/3#radians.

First, we have to find the measure of the third corner.

The sum of the angles in any triangle is #180^o# or #pi# radians.
Therefore, #pi-pi/12-(7pi)/12#

#=pi-(8pi)/12#

#=pi-(2pi)/3#

#=(3pi)/3-(2pi)/3#

#=pi/3#

So the measure of the third angle is #pi/3#.

Therefore, its complement is equal to:

#pi/2-pi/3=pi/6#radians.

And its supplement is equal to:

#pi-pi/3=(2pi)/3#radians.