Definition:
Two angles is called a supplementary angles if the sum of two angles equal to 180º or two right angles or straight angle.
Look at the following figure.
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
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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