Related Angles are the pair of angles that are related to each other. For each pair of related angles, there is a particular name given to them. These angles are related to each other based on some specific conditions.
Two angles are said to be related if they satisfy certain criteria. For example, when the transversal cuts the parallel lines, then there are certain angles that are formed such as corresponding angles, alternate interior angles, vertical angles, etc. Thus, these angles are related to each other with respect to the condition of transversal and parallel lines.
Types of Related Angles
The five types of related angles are:
Let us discuss all these related angles and their corresponding conditions by which they are related to each other.
Complementary Angles
The pair of angles that results in 90 degrees, when added together, are called complementary angles. Here, one angle is the complement of another angle. Hence, the complementary angles are related to each other by 90 degrees.
In simple words, when the sum of two angles is equal to 90Â°, then they are known as complementary angles. The examples of complementary angles are:
 30Â° and 90Â° (30Â° angle is the complement of 90Â°angle)
 20Â° and 70Â° (70Â°angle is the complement of 70Â° angle)
 40Â° and 50Â° (40Â° angle is the complement of 50Â° angle)
Facts:

Supplementary Angles
When the sum of any two angles is equal to 180 degrees, then such pairs of angles are called supplementary angles. In this case, one angle is said to be a supplement of the other. Thus, the supplementary angles are related to each other by 180 degrees.
The examples of supplementary angles are:
 60Â° and 120Â° (since 60Â° angle is the supplement of 120Â° angle)
 100Â° and 80Â° (since 100Â° angle is the supplement of 80Â° angle)
 90Â° and 90Â° (since 90Â° angle is the supplement of another 90Â° angle)
Facts:

Adjacent Angles
Two angles are said to be adjacent angles when they have a common vertex and a common arm. There shall be no common interior points between them.
The adjacent angles have common vertex, common arm but the noncommon arms are on either side of the common arm. See the below figure to understand the difference between adjacent and nonadjacent angles.
In the above figure, angle c and angle d are adjacent angles.
Angle x and angle y are nonadjacent angles
Also, although angle a and angle b have common vertices, they are still nonadjacent angles.
Linear Pair
We have learned about the adjacent angles in the above section. Now, if two adjacent angles together form a straight angle or 180 degree angle, then they are said to be a linear pair.
The noncommon sides of the linear pair of angles are opposite rays. Also, the angles in a linear pair are supplementary to each other. Thus, linear pairs are related angles.
The examples of linear pair of angles are:
 60Â° and 120Â° (with one arm and vertex common to each other)
 100Â° and 80Â° (with one arm and vertex common to each other)
 90Â° and 90Â° (with one arm and vertex common to each other)
Facts:

Vertically Opposite Angles
When two lines intersect or meet each other at a single point, then the vertically opposite angles formed are equal.
To be noted, there are four angles formed when two lines cut each other at a point. Thus, vertical angles that are opposite to each other at that point are equal. Therefore, such angles are related to each other in these terms. See the figure below, to understand better.
In the above figure, four angles are formed by the intersection of two lines, such that:
âˆ a = âˆ c
âˆ b = âˆ d
Some More Related Angles
Solved Examples
Q.1: What is the complement of 33Â°?
Solution: Let the required angle be x
Thus,
X + 33Â° = 90Â° [Complementary angles condition]
X = 90Â° – 33Â°
X = 57Â°
Therefore, the complement of 33Â° is 57Â°.
Q.2: What is the supplement of angle equal to 105Â°?
Solution: Let the required angle be x.
So,
X + 105Â° = 180Â° [Supplementary angles condition]
X = 180Â° – 105Â°
X =75Â°
Therefore, 75Â° and 105Â° are supplementary angles.
Practice Questions

Frequently Asked Questions on Related Angles
What are related angles?
Related Angles are the pair of angles that are related to each other based on certain conditions.
What are the five types of related angles?
The five types of related angles are:
Complementary angles
Supplementary angles
Adjacent angles
Linear Pair
Vertically opposite angles
What is the complementary angle of 20Â°?
The complement of 20Â°is 70Â°. Since, 90Â° â€“ 20Â° = 70Â°.
Are the linear pairs of angles more than 180 degrees?
No, the linear pair of angles are equal to 180 degrees.
How vertically opposite angles are formed?
When two lines intersect each other at a single point, then the vertically opposite angles formed are equal.