Question

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

Answer 1

`(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`