A triangle has two corners of angles #(pi )/4# and #(7 pi)/12 #. What are the complement and supplement of the third corner?

Question

A triangle has two corners of angles #(pi )/4# and #(7 pi)/12  #.  What are the complement and supplement of the third corner?

Evelyn Arboleda · Accepted Answer

#pi/3 , (5pi)/6# The sum of the 3 angles in a triangle is #pi# To find the 3rd angle , sum the 2 given angles together and subtract result from #pi# #rArrpi-(pi/4+(7pi)/12)=pi-(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# #rArrpi/2-pi/6=pi/3" is the complement of the 3rd angle"# #•"Supplementary angles are 2 angles whose sum is "pi# To find the supplement of a given angle subtract it from #pi# #rArrpi-pi/6=(5pi)/6" is the supplement of the 3rd angle"#

Claire Akin · Answer

undefined The sum of the angles in a triangle is always $ \pi $ radians (180 degrees). Therefore, to find the measure of the third angle in the triangle with angles $ \frac{\pi}{4} $ and $ \frac{7\pi}{12} $, you can subtract the sum of these two angles from $ \pi $.

$$ \text{Third angle} = \pi - \left( \frac{\pi}{4} + \frac{7\pi}{12} \right) $$

Once you have the measure of the third angle, you can find its complement and supplement by subtracting its measure from $ \frac{\pi}{2} $ (90 degrees) for the complement and $ \pi $ (180 degrees) for the supplement.