A triangle has two corners of angles #(pi )/6# and #(7pi)/12 #. What are the complement and supplement of the third corner?

1 Answer
Jun 2, 2016

Complement: #pi/4color(white)("XXXXXX")#Supplement: #(3pi)/4#

Explanation:

If two angles of a triangle are #pi/6# and #(7pi)/12#
the third angle must be
#color(white)("XXX")pi-(pi/6+(7pi)/12)=pi-(9pi)/12=pi/4#

Complementary angles add up to #pi/2#
so the complement of the third angle must be #pi/2-pi/4=pi/4#

Supplementary angles add up to #pi#
so the supplement of the third angle must be #pi=pi/4=(3pi)/4#