How do you find the complement and supplement of #pi/12#?

1 Answer
Mar 21, 2018

#(5pi)/12# radians or 75 degrees (complement), #(11pi)/12# radians or 165 degrees (supplement)

Explanation:

Complementary: angle measures add up to 90 degrees

Supplementary: angle measures add up to 180 degrees

Radians per full circle (360 degrees): #2pi#

Radians per half circle (180 degrees): #pi#

Radians per quarter circle (90 degrees): #1/2pi#

Complementary angle measure:

#x+pi/12=1/2pi rarr# #x# represents the unknown angle measure

#(12x)/12+pi/12=(6pi)/12#

#12x+pi=6pi#

#12x=5pi#

#x=(5pi)/12 rarr# Complementary angle measure in radians

To convert the angle measure to degrees, divide by #pi/180#

Supplementary angle measure:

#y+pi/12=pi rarr# #y# represents the unknown angle measure

#(12y)/12+pi/12=(12pi)/12#

#12y+pi=12pi#

#12y=11pi#

#y=(11pi)/12 rarr# Supplementary angle measure in radians

To convert the angle measure to degrees, divide by #pi/180#