Supplementary Angles

Definition:

Two angles is called a supplementary angles if the sum of two angles equal to 180º or two right angles or straight angle. 

These two angles can be separated or in the same figure. As long as the sum of these two angles is equal to 180º, the angles can be called as a complementary angles. 

Look at the following figure.

            Adjacent angles        on Adjacent angles

important note:

if aº is the given angle then angle bº become the supplement and its corollary. Since aº + bº = 180º then the value of the supplement of angle aº or can be written bº = 180º - aº.

Example 1.

It is given two angles x and y are supplementary angles. The magnitude of angle y is 124º. Determine the magnitude and the complement of angle x.

Solution:

if angles x and y are supplementary angles then x + y = 180º.

Since it is given y = 124º then 

x + 124º = 180º and 

x = 180º - 124º

x = 56º

if a is the complement of angle x then 
a = 90º - x
a = 90º - 56º
a = 34º

Magnitude of angle x is 56º and the complement is 34º.

Example 2.

Angles p and q are supplementary angles. if 1/3 magnitude of angle q is 1/6 of its supplement. Determine the magnitude of each angles.

Solution:

p and q are complementary angles then p + q = 180º.

q is the given angle than p is the supplement then p = 180º - q.

The mathematics model of "1/3 magnitude of angle q is 1/6 of its supplement" is:

q/3 = 1/6(180º - q)

2q = 180º - q

3q = 180º

q = 180º/3

q = 60º

p = 180º - q

p = 180º - 60º

p = 120º.

Then the magnitude of angle p = 120º and q = 60º.

  

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