What is two adjacent supplementary angles are called?

Two angles are said to be adjacent if they share a common arm and a common vertex between them. In simple words angles that are formed side by side are called adjacent angles. One of the main features of adjacent angles is that they do not overlap. Angles that are not adjacent are called nonadjacent angles.

The figure above shows two adjacent angles having a common side and a common vertex.

Are Adjacent Angles Complementary or Supplementary

Adjacent angles can be both complementary and supplementary. When the two angles add up to 90° it is called adjacent complementary angles, whereas when the two angles add up to 180° it is called adjacent supplementary angles. Two adjacent supplementary angles form a linear pair.

See our Complementary and Supplementary Angles article for more details.

How to Find Adjacent Angles

To identify whether the angles are adjacent or not, we must remember its basic properties that are given below:

• They should share a common arm between them
• They should share a vertex between them
• They should not overlap
• They should have a non-common arm on both the sides of the common arm

Are Adjacent Angles Congruent

Adjacent angles are congruent only when their common side bisects their sum. This happens when:

• A right angle is bisected to from two adjacent angles each measuring 45°
• A straight angle is bisected to from two adjacent angles where each of them is a right angle measuring 90°

In fig. 1 if the ray OP is rotated in the direction of the ray OQ, then the measure of its rotation represents the angle formed by it. In this case, the measure of rotation which is the angle formed between the initial side and the terminal side is represented by Ɵ.

Complementary Angles

When the sum of two angles is 90°, then the angles are known as complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Here we say that the two angles complement each other.

How to Find Complementary Angles?

Suppose if one angle is x then the other angle will be 90° – x. Hence, we use these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio by 90 degrees such as;

• sin (90° – A) = cos A and cos (90° – A) = sin A
• tan (90° – A) = cot A and cot (90° – A) = tan A
• sec (90° – A) = cosec A and cosec (90° – A) = sec A

Hence, you can see here the trigonometric ratio of the angles gets changed if they complement each other.

In the above figure, the measure of angle BOD is 60° and angle AOD measures 30°. By adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary angles.

The following angles in Fig. 3 given below are complementary to each other as the measure of the sum of both the angles is 90°. ∠POQ and ∠ABC are complementary and are called complements of each other.

For example: To find the complement of 2x + 52°, subtract the given angle from 90 degrees.

90o –  (2x + 52o) =  90o – 2x – 52o  = -2x + 38o 

The complement of 2x + 52o is 38o – 2x.

Supplementary Angles

When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.

How to Find Supplementary Angles?

The two angles form a linear angle, such that, if one angle is x, then the other the angle is 180° – x. The linearity here proves that the properties of the angles remain the same. Take the examples of trigonometric ratios such as;

• Sin (180 – A) = Sin A
• Cos (180 – A) = – Cos A (quadrant is changed)
• Tan (180 – A) = – Tan A

In Fig. 4 given above, the measure of ∠AOC is 60o and ∠AOB measures 120o. By adding both of these angles we get a straight angle. Therefore, ∠AOC and ∠AOB are supplementary angles, and both of these angles are known as a supplement to each other.

Also, learn:

• Adjacent Angles Vertical
• Lines And Angles

Difference between Complementary and Supplementary Angles

How to remember easily the difference between Complementary angles and supplementary angles?

• “C“ letter of Complementary stands for “Corner” (A right angle, 90°)
• “S“ letter of Supplementary stands for “Straight” ( a straight line, 180°)

Video Lesson on Types of Angles

Solved Examples

The example problems on supplementary and complementary angles are given below:

Example 1:

Find the complement of 40 degrees.

Solution: 

As the given angle is 40 degrees, then,

The complement is 50 degrees.

We know that sum of complementary angles =  90 degrees

So, 40° + 50° = 90°

Example 2:

Find the supplement of the angle 1/3 of 210°.

Solution: 

Step 1: Convert 1/3 of 210° 

That is, (1/3) x 210° = 70°

Step 2: Supplement of 70° = 180° – 70° = 110°

Therefore, the supplement of the angle 1/3 of 210° is 110°

Example 3: 

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

Solution: 

We know that, Sum of Supplementary angles =  180 degrees

So, 

(x + 25)° + (3x + 15)° = 180° 

4x + 40°  = 180° 

4x = 140° 

x = 35°  

The value of x is 35 degrees.

Example 4:

The difference between the two complementary angles is 52°. Find both the angles.

Solution: 

Let, First angle = m degrees, then,

Second angle =  (90 – m)degrees   {as per the definition of complementary angles}

Difference between angles = 52° 

Now,

 (90° – m) – m = 52° 

90° – 2m = 52° 

 – 2m = 52° – 90°

-2m = -38°

m = 38°/2°

m = 19°

Again, second angle = 90° – 19°  = 71° 

Therefore, the required angles are 19°, 71°.

Practice Questions

1. Check if 65° and 35° are complementary angles.
2. Are 80° and 100° supplementary?
3. Find the complement of 54°.
4. Find the supplement of 99°.
5. If one angle measures 50° and is supplementary to another angle. Then find the value of another angle. Also, state what type of angle it is?