# Complementary Angle

In English Vocabulary, “Complementary” means to complete something

In Math, two angles are complementary if they add up exactly to 90 degree.
The angles may or may not adjacent to each other.

When the angle make 90 degree it is known as right angle.
Hence, the complementary angles add up to form right angle.

Important keywords to remember Complementary Angle
⟹ Angle add up to 90 degree
⟹ Angles may not be adjacent

Examples of Complementary Angle

Example 01

From the above image you can observe that:
\angle a\ = 35 degree
\angle b\ = 55 degree

Adding both the angles we get:
\angle a\ + \angle b\ = 35 + 55
\angle a\ + \angle b\ = 90

Since both the angle add up to 90 degrees, they are complementary angles

Example 02
Complementary angles may not be adjacent to each other

Above image is of right angled triangle.

You can observe that angle A & C are separated from each other.
But if you add both of them, you will get 90 degree.

\angle A\ + \angle C\ = 50 + 40
\angle A\ + \angle C\ = 90

Hence, even if angle A & C are not adjacent they can be called complementary angles, since they add to give 90 degree measurement.

Example 03

Observe the above image:

From the above image you can observe that:
\angle A\ = 47 degree
\angle B\ = 43 degree

Adding both the angles we get:
\angle A\ + \angle B\ = 47 + 43
\angle A\ + \angle B\ = 90

Hence, both the angles are complementary

## Complementary Angles – Important Points

(a) When two angles are complementary, the angles are always acute

In Complementary angle;
\angle A\ + \angle B\ = 90

Since two angles are adding to give exactly 90 degree, this means that both the angles are less than 90 degree (hence acute)

(b) Obtuse angle cannot have a complement pair

Since obtuse angle is greater than 90 degree, it cannot satisfy the condition of complementary angle

## Frequently Asked Question: Complementary Angles

(01) Are complementary and supplementary angles same?

NO!!
Complementary Angle: sum of angle is 90 degree
Supplementary Angle : sum of angle is 180 degree

(02) The sum of two angle is 91.5 degree. Are the angles complementary?

NO!!
Sum has to be exactly 90 degree

(03) Should Complementary angles adjacent to each other?

Not Required
Two separated angles can be complementary

(04) Any real life example of complementary angle?

Take a piece of bread and cut through its diagonal, you will get a right angle triangle.

And in right angle triangle, we know the sum of other two angle is 90 degree.

(05) Find the complement of 95 degree

The angle is greater than 90 degree
Hence, its complement is not possible

## Complementary Angles Solved Question

(01) Given angle a & b are complementary angles
Find the value of angle b

As both angles are complementary, the sum of angle will be 90 degree

\angle a\ + \angle b\ = 90
40 + \angle b\ = 90
\angle b\ = 90 – 40
\angle b\ = 50

Hence 50 degree is the solution

(02) Find the complement of angle 64 degree

Let the complement angle be x degree
Complement angles add up to 90 degree

x + 64 = 90
x = 90 – 64
x = 26 degree

Hence 26 degree is the complement of 64 degree

(03) Find the complement of angle 42 degree

Let the required angle be x degree

x + 42 = 90
x = 90 – 42
x = 48 degree

Hence 48 degree is complement of 42 degree

(04) The measure of two complementary angles are x + 15 and 2x+ 30.
Find the value of x

Sum of complementary is 90 degree

(x + 15) + (2x+30) = 90
3x + 45 = 90
3x = 45
x = 15

Hence, x = 15 is the right answer

(05) The difference of two complementary angles is 12 degree. Find both the angles

Let the first angle be x degree
And second angle be y degree

Since both angles are complementary
x + y = 90
y = 90 – x – – – -eq(1)

Now we can say that the two angles are x and 90 – x

Its given that the difference of complementary angle is 12 degree
x – (90 – x) = 12
x – 90 + x = 12
2x = 102
x = 51

Hence, the two angles are:
x = 51 degree
and, 90 – 51 = 39 degree

51 and 39 degree is the required solution