# Supplementary Angle

When two angles add up to 180 degree, it is known as Supplementary Angle.
These angles doesn’t need to be adjacent to each other.

Angle with 180 degree is called Straight Angle
Hence, the supplementary angles add up to form straight angle

Important points for supplementary angle:
⟹ Angle add up to 180 degree
⟹ Angle need not to be adjacent to each other

Examples of Supplementary angle

Example 01
Obtuse Angle + Acute Angle

In the above example, you can observe that:

From the above image you can observe that:
\angle A\ = 60 degree
\angle B\ = 120 degree

Adding both the angles we get:
\angle A\ + \angle B\ = 60 + 120
\angle A\ + \angle B\ = 180

Both the angles add up to 180 degree, hence they are supplementary angles.

From the above image you can see how the angles add up to form straight line of 180 degrees.

Example 02
Right Angle + Right Angle

From the above image you can observe that:
\angle A\ = 90 degree
\angle B\ = 90 degree

Adding both the angles we get:
\angle A\ + \angle B\ = 90 + 90
\angle A\ + \angle B\ = 180

Both the angles add up to form 180 degree, hence the angles are complementary.

One can conclude from the above calculation that two right angles form supplementary pairs

Example 03
Obtuse Angle + Obtuse Angle

The smallest value of Obtuse Angle is 91 degree

Taking two smallest obtuse angle:
\angle A\ = 91 degree
\angle B\ = 91 degree

Adding both the angles we get:
\angle A\ + \angle B\ = 91 + 91
\angle A\ + \angle B\ = 182

For angle to be supplementary, the addition should be exactly 180 degree.

From the above calculation we conclude that two obtuse angles cannot be supplementary angles

Example 04
Acute Angle + Acute Angle

The largest value of Acute Angle is 89 degree

Taking two smallest obtuse angle:
\angle A\ = 89 degree
\angle B\ = 89 degree

Adding both the angles we get:
\angle A\ + \angle B\ = 89 + 89
\angle A\ + \angle B\ = 178

For angle to be supplementary, the addition should be exactly 180 degree.

Hence, two acute angles cannot be supplementary angle

## Frequently Asked Questions – Supplementary Angle

(01) Are complementary and supplementary angle same?

NO!!
When sum of angle is exactly 90 degree then its complementary angle
When sum of angle is exactly 180 degree then its supplementary angle

(02) The sum of two angle is 181 degree; Are the angles supplementary?

NO!
For supplementary, the sum should be exactly 180 degree

(03) Should supplementary angle adjacent to each other

NO!!
Two separate angles can be supplementary

(04) Real life example of supplementary angle

Take a chess board.
The side angle of the chess board is 90 degree.
Add the two sides and you will get supplementary angles

Observe the below clock

The above position of Hour, Minute and Second hand is such that they form supplementary angle.

(05) What is supplement of 181 degree?

The supplement of 181 degree is not possible as the angle is already above 180 degree

## Supplementary Angles Solved Question

(01) If angle A & B are supplementary angles, Find the value of angle B

As both angles are supplementary, the sum of angle will be 180 degree

\angle A\ + \angle B\ = 180
65 + \angle B\ = 180
\angle B\ = 180 – 65
\angle B\ = 115

Hence 115 degree is the solution

(02) Find the supplement of angle 36 degree

Let the supplement angle be x degree
Supplement angles add up to 180 degree

x + 36 = 180
x = 180 – 36
x = 144 degree

Hence 144 degree is the supplement of 36 degree

(03) Find the supplement of angle 100 degree

Let the supplement angle be x degree
Supplement angles add up to 180 degree

x + 100 = 180
x = 180 – 100
x = 80 degree

Hence 80 degree is the supplement of 100 degree

(04) The two supplementary angles are 3x + 40 and 2x + 15
Find the value of x

Supplementary angles add to 180 degrees

(3x+ 40) + (2x+15) = 180
5x + 55 = 180
5x = 125
x = 25

Hence, the value of x is 25

(05) The difference of supplementary angle is 50 degree. Find both the angles

Let the two angles be x & y

We know that supplementary angle add to 180 degree
x + y = 180
y = 180 – x —–eq(1)

Hence, he two angles can be written as x & 180 – x

Its given that difference of supplementary angle is 50 degree
x – (180 – x) = 50
x – 180 +x = 50
2x = 230
x = 115 degree

Hence the two angles are:
x = 115 degree
y = 180 -115 = 65 degree