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

1 Answer
May 4, 2016

complement: #0#
supplement: #pi/2 = 90^@#

Explanation:

Two angles are complementary if the add up to #pi/2 = 90^@#.
Two angles are supplementary if they add up to #pi = 180^@#

Since the interior angles of a triangle add up to #pi=180^@#
if two angles of a triangle are #pi/8# and #(3pi)/8#
then the third angle will be
#color(white)("XXX")pi - (pi/8+(3pi)/8) = pi/2=90^@#

and
#color(white)("XXX")#the complement of this third angle will be #0#
and
#color(white)("XXX")#the supplement of this third angle will be #pi/2=90^@#