Complementary and Supplementary Angles are the angles formed by adding two angles. If the sum of the two angles is 90º, they are called Complementary angles. Or else, if the sum of the two angles is 180º, they are called Supplementary angles. Find different problems on Supplementary and Complementary Angles in this article. Also, we have given all the concepts available in **Lines and Angles** on our website.

### Complementary Angles

The two angles are said to be complementary angles if their sum is one right angle i.e. 90°. Each angle is called the complement of the other. If x° is one angle then (90 – x)° is the other angle in Complementary Angles.

For example, if 70° is one angle in Complementary Angles, then the other angle will be 20°. 70° and 20° complement each other.

Example 1: To find the complement of 3y + 52°, subtract the given angle from 90 degrees.

90º – (3y + 52º) = 90º – 3y – 52º = -3y + 38º

The complement of 3y + 52° is 38º – 3y.

#### Facts of complementary angles

- Two complementary angles are acute but vice versa is not possible
- Two right angles cannot complement each other
- Also, two obtuse angles cannot complement each other

### Supplementary Angles

The two angles are said to be Supplementary angles if their sum is 180°. Two angles are added and formed a straight line in Supplementary Angles. If x is one angle then (180 – x)° is the other angle in Supplementary Angles.

For example, if 130° is one angle in Supplementary Angles, then the other angle will be 50°. By adding 130 and 50 degrees, it forms a straight line. In Supplementary Angles, both angles are said to be a supplement to each other.

### Solved Examples on Supplementary and Complementary Angles

1. Find the complement of 50 degrees?

Solution:

The given angle is 50 degrees, then, the Complement is 40 degrees.

We know that Sum of Complementary angles = 90 degrees.

By adding 40 degrees to 50 degrees, the total angle becomes 90 degrees.

So, 50° + 40° = 90°

The final answer is 90°

2. Find the Supplement of the angle 1/4 of 200°.

Solution:

Given that the angle 1/4 of 200°

Convert 1/4 of 200°

That is, 1/4 x 200° = 50°

Supplement of 50° = 180° – 50° = 130°

By adding 130 degrees to 50 degrees, the total angle becomes 180 degrees.

Therefore, Supplement of the angle 1/4 of 200° is 130°

3. The measures of two angles are (x + 15)° and (3x + 25)°. Find the value of x if angles are supplementary angles.

Solution:

We know that, Sum of Supplementary angles = 180 degrees.

So, (x + 15)° + (3x + 25)° = 180°

Add the x terms and numbers.

4x + 40° = 180°

Move 40° to the right side and subtract it from 180°.

4x = 140°

Move 4 to the right side and divide it from 140°.

x = 35°

The value of x is 35 degrees.

4. The difference between two complementary angles is 54°. Find both the angles.

Solution:

Given that the difference between two complementary angles is 54°.

Let, the first angle = x degrees, then, Second angle = (90 – x)degrees {as per the definition of complementary angles}

Difference between angles = 54°

Now, (90° – x) – x = 54°

90° – 2x = 54°

– 2x = 54° – 90°

-2x = -36°

x = 36°/2°

x = 18°

Again, Second angle = 90° – 18° = 72°

Therefore, the required angles are 18°, 72°.

5. Find the complement of the angle 4/5 of 90°.

Solution:

Convert 4/5 of 90°

Multiply 4/5 with 90°

4/5 × 90° = 72°

Complement of 72° = 90° – 72° = 18°

Therefore, a complement of the angle 4/5 of 90° = 18°

6. Find the supplement of the angle 2/3 of 90°.

Solution:

Convert 2/3 of 90°

2/3 × 90° = 60°

Supplement of 60° = 180° – 60° = 120°

Therefore, a supplement of the angle 2/3 of 90° = 120°

7. The measure of two complementary angles are (3x – 6)° and (x – 4)°. Find the value of x.

Solution:

According to the problem, (3x – 6)° and (x – 4)°, are complementary angles’ so we get;

(3x – 6)° + (x – 4)° = 90°

or, 3x – 6° + x – 4° = 90°

or, 3x + x – 6° – 4° = 90°

or, 4x – 10° = 90°

Add 10° on both sides.

or, 4x – 10° + 10° = 90° + 10°

or, 4x = 100°

or, x = 100°/4°

or, x = 25°

Therefore, the value of x = 25°.