How do you find the complement and supplement of angles?

Question

i need help in finding the complement and supplement of angles measured in degrees and radians.
example: 35.5 degrees
example: 5[pi] / 6

Answer 1

Complementary angles sum to 90 degrees (or pi/2 radians)
Supplementary angles sum to 180 degrees (or pi radians)

Example 1:
Let c be the complementary angle:
35.5 + c = 90
c = 90 - 35.5
c = 54.5 degrees

Let s be the supplementary angle:
35.5 + s = 180
s = 180 - 35.5
s = 144.5 degrees

Example 2:
5(pi)/6, well this is bigger than pi/2, so it won't have a complementary angle.

Let s be the supplementary angle.
(5/6)pi + s = pi
s = pi - (5/6)pi
s = (1 - 5/6)pi
s = (1/6)pi

To convert, remember that the full circle is 360 degrees, and it is also 2pi radians. So pi radians = 180 degrees. pi/2 radians = 90 degrees.

(1/6)pi radians * 180/pi = 30 degrees

Answer 2

Supplentary angles add up to 180 degrees.
Ex. 130 and 50 (subtract the given angle from 180 to find its supplement)

Complementary angles add up to 90 degrees.
Ex. 25 and 65 (subtract the given angle from 90 to find its complement)

To convert radians to degrees - multiply radians by 180/pi
the pi's will drop out and you will have degrees.

To convert degrees - multiply degrees by pi/180

Answer 3

-3/5 pie