A triangle has two corners of angles #pi /8# and #(3pi)/4 #. What are the complement and supplement of the third corner?

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Answer 1 · 2016-12-19T21:21:31

complement = #(3pi)/8#
supplement = #(7pi)/8#

#sum#(angles in a #triangle#) = #180^@#, or #pi#

third corner = #pi# - (first corner + second corner)

# = pi - (pi/8 + 3pi/4)#

#= (8/8)pi - (1/8)pi + (6/8)pi#

# = pi/8#

complements add to #0.5pi#

#0.5pi = pi/2 = (4pi)/8#

complement of #pi/8# = #(4pi/8) - pi/8# = #3pi/8#

supplements add to #pi#

#8pi/8# - #pi/8# = #7pi/8#