A triangle has two corners of angles #pi /8# and #(7pi)/12 #. What are the complement and supplement of the third corner?

Question

A triangle has two corners of angles #pi /8# and #(7pi)/12  #.  What are the complement and supplement of the third corner?

Maverick Smith · Accepted Answer

#(5pi)/24" and " (17pi)/24# The sum of the 3 angles in a triangle #=pi# To calculate the third angle, subtract the sum of the 2 given angles from #pi# #"third angle " =pi-(pi/8+(7pi)/12)# #=pi-((3pi)/24+(14pi)/24)=pi-(17pi)/24# #=(24pi)/24-(17pi)/24=(7pi)/24larrcolor(red)"third angle"# An angle and it's #color(blue)"complement"# sum to #pi/2# #"complement of " (7pi)/24=(pi/2-(7pi)/24)# #=(12pi)/24-(7pi)/24=(5pi)/24larrcolor(red)"complement"# An angle and it's #color(blue)"supplement"# sum to #pi# #"supplement of " (7pi)/24=(pi-(7pi)/24)# #=(24pi)/24-(7pi)/24=(17pi)/24larrcolor(red)"supplement"# #color(blue)"As a check"# #(7pi)/24+(5pi)/24=(12pi)/24=pi/2color(white)(x)✔︎# #"and " (7pi)/24+(17pi)/24=(24pi)/24=picolor(white)(xx)✔︎#

Avery Allen · Answer

undefined The sum of the angles in a triangle is always $ \pi $ radians (180 degrees). So, to find the measure of the third angle, subtract the measures of the given angles from $ \pi $:

$ \text{Third angle} = \pi - \left( \frac{\pi}{8} + \frac{7\pi}{12} \right) $

To find the complement of an angle, subtract its measure from $ \frac{\pi}{2} $ (90 degrees). To find the supplement of an angle, subtract its measure from $ \pi $ (180 degrees).