How do you find the complement and supplement of $\frac{π}{12}$ $pi/12$ ?

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Answer 1 · 2018-03-21T23:45:15

$\frac{5 π}{12}$ $(5pi)/12$ radians or 75 degrees (complement), $\frac{11 π}{12}$ $(11pi)/12$ 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): $2 π$ $2pi$

Radians per half circle (180 degrees): $π$ $pi$

Radians per quarter circle (90 degrees): $\frac{1}{2} π$ $1/2pi$

Complementary angle measure:

$x + \frac{π}{12} = \frac{1}{2} π \to$ $x+pi/12=1/2pi rarr$ $x$ $x$ represents the unknown angle measure

$\frac{12 x}{12} + \frac{π}{12} = \frac{6 π}{12}$ $(12x)/12+pi/12=(6pi)/12$

$12 x + π = 6 π$ $12x+pi=6pi$

$12 x = 5 π$ $12x=5pi$

$x = \frac{5 π}{12} \to$ $x=(5pi)/12 rarr$ Complementary angle measure in radians

To convert the angle measure to degrees, divide by $\frac{π}{180}$ $pi/180$

Supplementary angle measure:

$y + \frac{π}{12} = π \to$ $y+pi/12=pi rarr$ $y$ $y$ represents the unknown angle measure

$\frac{12 y}{12} + \frac{π}{12} = \frac{12 π}{12}$ $(12y)/12+pi/12=(12pi)/12$

$12 y + π = 12 π$ $12y+pi=12pi$

$12 y = 11 π$ $12y=11pi$

$y = \frac{11 π}{12} \to$ $y=(11pi)/12 rarr$ Supplementary angle measure in radians

To convert the angle measure to degrees, divide by $\frac{π}{180}$ $pi/180$

How do you find the complement and supplement of π12pi/12?