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

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Answer 1 · 2018-03-21T23:45:15

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

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 $pi/180$

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