Complementary Angles

Definition:

Two angles is called a complementary angles if the sum of two angles equal to 90º.

These two angles can be separated or in the same figure. As long as the sum of these two angles is equal to 90º, the angles can be called as a complementary angles. Look at the following figure.

              Adjacent angles     Non Adjacent angles

important note:

if aº is the given angle then angle bº become the complement and its corollary. Since aº + bº = 90º then the value of the complement of angle aº or can be written bº = 90º - aº.

Example 1.

It is given two angles x and y are complementary angles. The magnitude of angle x is 34º. Determine the value of angle y.

Solution:

if angles x and y are complementary angles then x + y = 90º.

Since it is given x = 34º then 

34º + y = 90º and 

y = 90º - 34º

y = 56º

Magnitude of angle y is 56º.

Example 2.

Angles p and q are complementary angles. Magnitude of angle q is 1/4 of its complement. Determine the magnitude of each angles.

Solution:

p and q are complementary angles then p + q = 90º.

q is the given angle than p is the complement then p = 90º - q.

The mathematics model of "Magnitude of angle q is 1/4 of its complement" is:

q = 1/4(90º - q)

4q = 90º - q

5q = 90º

q = 90º/5

q = 18º

p = 90º - q

p = 90º - 18º

p = 72º.

Then the magnitude of angle p = 72º and q = 18º.

  
Example 3.

Look at the following figure.

if angle ABD = (5x - 1)º and angle CBD = (2x + 7)º. These angles are also complementary angles. Determine the magnitude of each angle.

Solution:

ABD = (5x - 1)º

CBD = (2x + 7)º

ABD and CBD are complementary angles then ABD + CBD = 90º.

ABD + CBD = 90º

(5x - 1)º + (2x + 7)º = 90º    
7x + 6 = 90º
7x = 84º
x = 12º

ABD = (5x - 1)º
ABD = 5.12 - 1 = 59º
 

CBD = (2x + 7)º

CBD = 2.12 + 7 = 31º

-Vn-