In Geometry, we use the term pair of angles for two angles that are related to each other. We study these pairs of angles to understand the relationship between different types of angles. There are different pairs of angles like supplementary angles, complementary eagles, adjacent angles, interior angles, and many more. In this blog, we are going to study supplementary angles in detail. We will explore various properties and characteristics of supplementary angles. Let us begin by understanding what a supplementary angle actually is.
What are Supplementary Angles?
An angle is a figure that is formed by two rays which are also known as the sides of the angle. The common endpoint shared by these angles is known as the vertex of an angle. Supplementary angles refer to a pair of two angles forming a straight angle at 180 degrees when they are put together. Thus these two angles are known as the supplements of each other. Measuring angles and & finding angles are the most frequent steps carried out in geometry. However, to do so, one needs to understand the relationship between angles. Hence we study supplementary angles.
Trick to Remember Supplementary Angles
Many students get confused between complementary and supplementary angles. So here is a simple trick to remember supplementary angles. Since “S” is for “Supplementary” and “S” is for “Straight.” Hence, you can remember that two “Supplementary” angles, when put together, form a “Straight” angle.
If you want to learn the concept of supplementary angles with some interesting tips and tricks, you can take the help of Cuemath math worksheets. Cuemath helps students understand the concept of supplementary angles through modern learning techniques like visualization, math games, etc. This makes math super interesting and fun.
Let us now explore the various characteristics of supplementary angles:
Characteristics of Supplementary Angles
- Two angles that sum to a straight angle (turn, 180°) are called supplementary angles.
- Adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary.
- The sines of supplementary angles are equal.
- In geometry, any sum of two angles in a triangle is supplementary to the third because the sum of internal angles of a triangle is a straight angle.
Example of Supplementary Angles
Two Angles are said to be supplementary pairs of angles when their sum equals 180 degrees. These angles do not necessarily have to be placed next to each other. For e.g., 60° and 120° are supplementary angles as after adding them up; the sum equals a total of 180 degrees.
Types of Supplementary Angles
Now that we have studied supplementary angles in detail, let us explore some of the types of supplementary angles. In order to understand the types of supplementary angles, let us go through the following two theorems :
Theorem 1): If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles.
Theorem 2): If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles.
Supplementary angles are also classified as:-
- Adjacent supplementary angles
- Non- adjacent supplementary angle
Adjacent Supplementary Angles
Two supplementary angles with a common vertex and a common arm are said to be adjacent supplementary angles.
Non- Adjacent Supplementary Angles
Two angles that do not have a common ray coming out of the vertex going between two other rays are called non-adjacent angles. If the sum of two non-adjacent angles, A and B, is 180 degrees, then those angles A and B are called non-adjacent supplementary angles where A is known as the supplement of B, and B can be called the supplement of A.