What is a Linear Pair?

When dealing with angles, it is important to understand the various geometric relationships that can exist between them. One of these relationships is a linear pair of angles. In this article we will discuss the definition of a linear pair of angles, the characteristics of one, and the different types of linear pairs.

Definition of a Linear Pair of Angles

A linear pair of angles is a pair of adjacent (or connected) angles whose non-common sides form a straight line. The two lines intersecting at the vertex of the angle form a right angle. A right angle is an angle that measures exactly 90°. Because the non-common sides form a straight line, the measurement of the two angles will add up to 180°.

Characteristics of a Linear Pair of Angles

There are a few basic characteristics that are associated with a linear pair of angles. First, the two angles must be adjacent and their non-common sides must form a straight line. The two angles must also add up to form a right angle, or 90°. Lastly, the total measure of both angles will always equal 180°.

Types of Linear Pairs

There are four different types of linear pairs.

1. Supplementary Linear Pair: A supplementary linear pair is comprised of two angles that add up to form a straight line and the sum of the angles measure exactly 180°. Examples of this type of linear pair include: a 90° angle and a 90° angle, or a 60° angle and a 120° angle.

2. Complementary Linear Pair: A complementary linear pair is formed when two angles add up to a straight line and the sum of the angles measure exactly 90°. Examples of this type of linear pair include: an 85° angle and a 5° angle, or a 30° angle and a 60° angle.

3. Adjacent Linear Pair: An adjacent linear pair is formed when two angles are adjacent to one another, but the sum of their measure does not add up to 90° or 180°. Examples of this type of linear pair include: a 45° angle and a 65° angle, or a 80° angle and a 40° angle.

4. Vertical Linear Pair: A vertical linear pair is formed when two angles are directly next to each other, and their sum adds up to form a right angle. Examples of this type of linear pair include: a 60° angle and a 30° angle, or a 45° angle and a 45° angle.

Conclusion

Linear pairs of angles are a common geometric relationship between two angles. Understanding the characteristics, definition, and types of linear pairs of angles can help to better understand the concept. With this understanding, it is possible to apply the information to solve various mathematical and geometry problems.