Pairs of Angles: Explanation, Types and Examples

Pairs of angles are generated when two lines have a common endpoint, termed the Vertex, and an angle is formed between these two lines. There is a unique connection between angle pairs. Some of the types of angle pairings are: Complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles, and adjacent angles.

Also Read: Angle Formula

Key Terms: Angles, Pairs of Angles, Complementary Angles, Supplementary Angles, Vertical Angles, Alternate Interior Angles, Alternate Exterior Angles, Corresponding Angles

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Types of Angels with Examples

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Complementary Angles

Complementary angles are formed when the total of two angles equals 90 degrees. Each angle is referred to as the complement of the other. As seen in the diagram below,

Complementary Angles

Therefore, ∠AOD and ∠BOD are complementary angles.

More Examples:

• 50° and 40° (50° + 40° = 90°)
• 75° and 15° (75° + 15° = 90°)
• 55° and 35° (55° + 35° = 90°)

Supplementary Angles

Supplementary Angles are formed by two angles whose sum equals 180 degrees.

Supplementary Angles

Therefore, ∠P and ∠R are Supplementary angles of each other.

More Examples:

• 150° and 30° (150° + 30° = 180°)
• 50° and 130° (50° + 130° = 180°)

Difference Between Complementary Angle and Supplementary Angle

Key differences between complementary and supplementary angles are tabulated below:

Adjacent Angles

Adjacent angles are any two angles that have a common side, a shared vertex, and do not overlap. In the figure, ∠CAD and ∠BAD are adjacent angles.

Adjacent angles

Conditions two angles need to fulfil to be Adjacent angles:

• have a common side
• Have a common vertex
• no overlap

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Linear Pair of Angles

The adjacent angles of two intersecting lines form a linear pair. The total of linear pairs equals 180 degrees. It's worth noting that all linear pairings are supplementary since the total of supplementary angles equals 180°. However, all supplementary angles do not have to be linear pairs because the lines in linear pairs must overlap to generate adjacent angles. In the diagram below, ∠1 and ∠2 form a linear pair, and their total is 180 degrees.

Linear Pair of Angles

Vertical Angles

A pair of non-adjacent angles created by the intersection of two Straight Lines is known as a vertical angle.

Vertical Angles

Here, line AD and line BC cross at one point, which we'll name X, resulting in four angles:

1. ∠AXB = θ₁
2. ∠BXD = θ₂
3. ∠DXC = θ₃
4. ∠CXA = θ₄

Because θ₁ and θ₂ are non-adjacent angles created by the intersection of lines AD and BC, they are always equal, implying that θ₁ = θ₂. In the same way, θ₃ and θ₄ are both vertical angles, hence θ₃ Equals θ₄.

Pairs of Angles Formed by Transveral

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Co-interior Angles

Co-interior angles are always supplementary when a transversal connects two parallel lines. Angles that are co-interior:

• Different vertices are present.
• Lie in the middle of two lines.
• Are on the same transverse side.

∠A and ∠C are co-interior angles in the diagram below. ∠B and ∠D are co-interior angles in the same way. As a result, they serve as an add-on.

Co-interior angles

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Alternate Interior Angles [Click Here for Sample Questions]

The alternate interior angles are created when a transversal meets two parallel lines. They are always equal. The angles that make up alternate-interior angles are those that:

• Different vertices are present.
• Lie on the transversal on opposite sides.
• Lie in the middle of the two lines.

In the figure below, ∠A and ∠D, ∠B and ∠C are the alternate interior angles.

Alternate Interior Angles

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Alternate Exterior Angles

The alternate exterior angles created by a transversal intersecting two parallel lines are always equal. Angles that are opposite to the exterior are known as alternate-exterior angles.

• Different vertices are present.
• Lie on the transversal on alternate sides.
• Lie on the exterior of the lines.

In the following figure, ∠1 & ∠8, ∠2 & ∠7 are alternate exterior angles.

Alternate Exterior Angles

Corresponding Angles [Click Here for Sample Questions]

The corresponding angles created by a transversal intersecting two parallel lines are always equal. The angles that correspond to each other are:

• Have a number of vertices.
• Lie on the same side of the transversal and above (or below) of the lines.

In the following figure, ∠1 & ∠5, ∠3 & ∠7 are pairs of corresponding angles that are equal.

Corresponding Angles

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Things to Remember

• Complementary angles are formed when the total of two angles equals 90 degrees. These angles don't have to be close to each other, but their sum should equal 90 degrees.
• Angles must have a common side and vertex to be considered adjacent.
• A linear pair must be supplementary, but a supplementary angle does not have to be. In either case, the sum of the angles should always be 180°.
• Linear pairings do not exist in all supplementary angles.
• Angles that are next to one another are not necessarily adjacent angles.
• If we have an x° angle, we can subtract it from 90° to obtain a complementary angle.
• If we have an x° angle, we can subtract it from 180° to find a supplementary angle. 

Also read:

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