If the sum of the measures of two angles is 180⁰,
then the angles are called supplementary angles.
Each angle is called the supplement of the other angle.
For example, if one angle measures 70⁰, then it's
supplement will measure 110⁰ (180-70).
Remember....
Supplementary angles are a pair of angles....
if more than 2 angles add up to 180⁰,
they are not supplementary!

This is a fairly basic concept.
However, there are lots of interesting problems
involving supplementary angles.

Let's look at a few.....

Two angles are supplementary. 
One of the angles is three times as large as the other. 
Find the measure of both angles.

Solution:
First, assign variables to represent the two angles.
Let x = the smaller angle
Let 3x = the larger angle
(remember...it is 3 times larger!)
Second, write the equation.
3x + x = 180
(the sum of the angles is 180⁰)
Third, solve the equation.
3x + x = 180
(combine like terms)
4x = 180
(divide both sides by 4)
x = 45
Therefore, the measure of the smaller angle (x) is 45⁰
and the measure of the larger angle (3x) is 135⁰.
(to check....just add 45 and 135...it equals 180⁰)

Let's look at another...

Find the number of degrees in an angle which is
20⁰ less than four times it's supplement.

Solution:
Let 4x - 20 =  one of the angles
Let x =the supplement of the angle
(4x-20) + (x) = 180
5x - 20 = 180
5x = 200
x = 40
Therefore, one of the angles (4x-20) is 140⁰,
and the supplement of that angle is (180 - 140) = 40⁰.

One final example.....

Find the supplement of the angle which is
represented by the expression (4x-60)⁰

For this problem let's use the fact that the easiest way to
find the supplement of an angle is to subtract the given angle from 180⁰.
So, if we let one of the angles be "x", and it's supplement be (4x-60)⁰,
then we should be able to find the other angle
by solving the following equation:
x = 180 - (4x - 60)
(distribute the "-" sign)
x = 180 - 4x + 60
(simplify)
x = 240 - 4x
(add 4x to both sides)
5x = 240
(divide by 5)
x = 48⁰
Let's see if it makes sense...
If one angle is (4x - 60), and x = 48
Substituting in that value we get..
(4(48) - 60)
192 - 60
132⁰
And as we can easily see...
48 + 132 = 180!
Therefore the supplement is 48⁰
 

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