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

1 Answer
Jun 29, 2018

The supplement of the third angle is #5/24pi#
It does not have a complement.

Explanation:

The sum of all 3 angles in any triangle is #pi# (or #180^0#)

So we find the third angle with this equation:

#pi/12 + pi/8 + x = pi#
#x=pi - 2/24pi - 3/24pi#
#x=19/24pi#

Two angles are complementary if the sum of the two angles adds up to #pi/2# (or #90^0#)

But this is an obtuse angle: # 19/24pi > pi/2#
so it does not have a complement.

Two angles are supplementary if the sum of the two angles adds up to #pi# (or #180^0#)
#19/24pi + S = pi#
#S = pi - 19/24pi#

The supplement angle is: #S = 5/24pi#