Introduction of Complementary Angle

The words "complere" and "plere" come from the Latin words "complere" and "plere," respectively, which mean "complete" and "fill." So complementary angles mean pair of two angles that sum up to 90°. Complementary angles form a right angle. 

For example: if you take a square cake and divtopicIde it into two pieces by cutting along the diagonal, two right angles triangles or formed each with a pair of 90° that is the complementary angle. So complementary angle means when two pairs of angles are added together and we get the sum as 90°.

The magic rule to find the complementary angle is to subtract the angle given by 90° and you will get the result. Isn’t it amazing !!!!

Definition of complementary angle

Two angles are satopicId to be complementary angles when they add it up to 90°.

For example: suppose angle one is 40° and angle two is 50°

                      Angle 1 + Angle 2 = 90°

                      40° +50° = 90°  (complementary angle) 

Here, 40° is a complement of 50° and 50° is a complement of 40°.

Example 1

Find the complementary angle for 35°.

90° -35° = 55°

So 55° is the complement angle of 35°.

Example 2 

Find compliment for 41°24’

= 90° - 41°24’

= 89°60’ - 41°24’ 

= 48°36’

Therefore the complement of 41°24’ is 48°36’

Example 3 

Check if 65° and 55° are complementary to each other or not? 

65° + 55° = 120° 

Since it is 120° ( which is more than 90°)  it does not complement to each other.

Example 4: 

If two angles are equal then find the complementary angles?

Let the first angle be x. Second angle will also be x

= x + x = 90°

=2x = 90°

= x = 90° divtopicIded by 2 

x = 45°

Therefore when two angles are equal then the total of first angle is 45° and second angle will also be 45°.

Features of complementary angle:

The following are the features of characteristics of the Complementary angle:

The sum of total of the two angles should always be 90° 

Complementary angles always have positive measures.

Complementary angles are always composed of two acute angles measuring less than 90°.

Some complementary angles are adjacent to each other while some are not adjacent to each other.

An angle measuring 1° would be the complement to the angle measuring 89°.

Any two or three triangles cannot be complementary angles if their sum is more than 90°.

The Greeks found complementary angles. 

Two right angles can’t complement each other.

Two obtuse angles can’t complement each other.

Any three or more Angles cannot be complimentary even if there is some is 90°.

Types of complementary angle:  

There are two types of complementary angles 

1) adjacent complementary angles

2) non-adjacent complementary angles.

Adjacent complementary angles: 

In any two complementary angles if they have one common vertex and common arms then they are called adjacent complementary angles. 

Non-adjacent complementary angles:

Two complementary angles if they are not adjacent to each other and they don’t share any common vertex and common arms then they are called non-adjacent complementary angles.