A triangle has two corners of angles #pi /6# and #(2pi)/3 #. What are the complement and supplement of the third corner?

1 Answer
Jun 14, 2016

compemeent #=pi/3#
supplement #=(5pi)/6#

Explanation:

The sum of the 3 angles in a triangle is #pi#

To find the 3rd angle , subtract the sum of the 2 given angles from #pi#

3rd angle #=pi-(pi/6+(2pi)/3)=pi-(pi/6+(4pi)/6)#

3rd angle #=pi-(5pi)/6=(6pi)/6-(5pi)/6=pi/6#
#"-----------------------------------------------------------"#
Complementary Angles are 2 angles whose sum is #pi/2#

To find the Complement of a given angle subtract it from #pi/2#

Complement of #pi/6=pi/2-pi/6=(3pi)/6-pi/6=(2pi)/6=pi/3#
#"--------------------------------------------------------------"#

Supplementary Angles are 2 angles whose sum is #pi#

To find the Supplement of a given angle subtract it from #pi#

Supplement of #pi/6=pi-pi/6=(6pi)/6-pi/6=(5pi)/6#