# Expert Maths Tutoring in the UK

Find the Angles – MUST know to PASS Geometry
Find the Angles – MUST know to PASS Geometry

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Adjacent angles are the angles that have a common arm (side) and a common vertex, however, they do not overlap. An angle is formed when two rays meet at a common endpoint and adjacent angles are those angles that are always placed next to each other. When the sum of two adjacent angles is 180° then they are called a linear pair of angles. Let us learn more about adjacent angles and see some adjacent angles examples in this page.

Two angles are said to be adjacent angles, if, they share a common vertex, a common side and they do not overlap. Observe the following figure to understand what adjacent angles look like. Angle 1 and 2 are adjacent because they have a common side BD and a common vertex B.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

We can see many real-life examples of adjacent angles.

• The most common real-life example of adjacent angles can be seen in two pizza slices that are placed next to each other.
• Another common example can be seen in the clock which shows the hour, minute, and second hand that form adjacent angles when all the 3 are away from each other.
• We can find 3 adjacent angles in the steering wheel of a car.

The properties of adjacent angles given below help us identify them easily.

• Adjacent angles always share a common arm.
• They share a common vertex.
• They do not overlap.
• They have a non-common arm on both sides of the common arm.
• Two adjacent angles can be supplementary or complementary based on the sum of the measures of the individual angles.

## How to Find Adjacent Angles?

Adjacent angles can be easily identified with the help of two main properties – adjacent angles always share a common side and a common vertex. If any two angles satisfy only one of these properties, they will not be considered adjacent angles. It is necessary for the angles to fulfill both the properties. For example, if any two angles share a common vertex, but they have an angle in between, this means that they are not sharing a common side. Hence, they cannot be adjacent angles. Observe the following figure to identify adjacent angles.

Important Notes

Here is a list of a few important notes related to the adjacent angles.

• When two angles are adjacent, then their sum is the angle formed by two non-common arms and one common arm.
• If a ray stands on a straight line, then the sum of adjacent angles formed is 180°.
• If the sum of two adjacent angles is 180° then they are called a linear pair of angles. All linear pairs are supplementary because supplementary angles sum up to 180°. However, all supplementary angles need not be linear pairs. To form a linear pair the lines need to intersect each other and must form adjacent angles.
• If the sum of two adjacent angles is 180° then the non-common arms form a line.

☛Related Articles

Check out these interesting articles to know more about Adjacent Angles and their related topics.

1. Example 1: List 5 pairs of adjacent angles in the following figure.

Solution: Five pairs of adjacent angles are given below.

∠AOE, ∠EOC

∠EOC, ∠COB

∠COB, ∠BOD

∠BOD, ∠AOD

∠AOD, ∠AOE

2. Example 2: Are the angles marked as 1 and 2 in the following figures adjacent? Give reasons for your answers.

Solution: Clearly ∠1, ∠2 have a common vertex O and a common ray OB. Therefore, ∠1, ∠2 are adjacent angles.

3. Example 3: State true or false with reference to the properties of adjacent angles.

a.) Adjacent angles are always supplementary.

b.) Adjacent angles always share a common vertex and a common arm.

c.)If two adjacent angles on a straight line are in the ratio 2 : 3, the measure of these angles is 72° and 108°

Solution:

a.) False, adjacent angles may not always be supplementary. If any two adjacent angles form a straight line together, then they form supplementary adjacent angles.

b.) True, adjacent angles always share a common vertex and a common arm.

c.)If two adjacent angles on a straight line are in the ratio 2 : 3, the measure of these angles is 72° and 108°

## Practice Questions on Adjacent Angles

### What are Adjacent Angles in Geometry?

Two angles are said to be adjacent angles, if, they have the following characteristics:

• They share a common vertex.
• They share a common side or ray.
• They do not overlap.

### Can 2 Adjacent Angles be Supplementary?

Yes, adjacent angles can be supplementary if they sum up to 180°. Adjacent angles can be defined as two angles that have a common vertex and a common side. Any two adjacent angles can be complementary angles or supplementary angles according to the sum of the measurement of angles.

### Can Vertical Angles be Adjacent?

No, vertical angles can never be adjacent. Adjacent angles are the two angles next to each other while vertical angles are opposite to each other.

### Give Some Examples of Adjacent Angles in Daily Life.

Adjacent angles can be commonly seen in our daily lives. For example, in the steering wheels of the car, the three hands of the clock, two pizza slices that are placed next to each other in the pizza box, and so on.

### Can 2 Adjacent Angles Overlap?

No, adjacent angles can never be one on top of the other, or in other words, the angles cannot overlap. The angles which are placed next to each other on one vertex and share one side are adjacent angles.

The sum of two adjacent angles can be either complementary or supplementary based on their measures. If two adjacent angles are placed next to each other on a straight line they will add up to 180° because these will be adjacent supplementary angles. If the adjacent angles do not form linear pairs, they will not add up to 180°.

What is the Difference Between Adjacent Angles and Linear Pair of Angles?

Adjacent angles may or may not form a straight line together. They just need to fulfill the property that they share a common vertex and a common side. However, linear pair of angles always form a straight line, and hence they always sum up to 180°.

### How to Identify Adjacent Angles?

Adjacent angles can be easily identified with the help of two main properties:

• Adjacent angles always share a common side.
• Adjacent angles always share a common vertex.

If any two angles satisfy only one of these properties, they will not be considered adjacent angles. It is necessary for the angles to fulfill both the properties.

### What is the Difference between Adjacent Angles and Vertical Angles?

Adjacent angles always share a common vertex and a common side and they do not overlap each other. Vertical angles are the angles that are formed when two lines intersect each other.

### What are Adjacent Angles in a Parallelogram?

Adjacent angles of a parallelogram are those angles that are located next to each other. They are also known as the consecutive angles of the parallelogram. The sum of these adjacent angles of a parallelogram is always 180°.

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