Introduction of Supplementary Angle  

The Latin words "Supplere" and "Plere," meaning "supply" and "fill," are the roots of the English word "supplementary." Supplementary angles mean when two angles are together and their total is equal to 180°. That means they form a straight line or look as good as a straight angle. 

To elaborate, if the two angles are supplementary to each other, they do not have to be next to each other. So, angles can turn out to be supplementary if their sum of the total angle is equal to 180°

Definition of supplementary angle

When two angles are added and their total is 180° then they are satopicId to be supplementary angles.

To simplify, when one angle + another angle = 180°, they are called supplementary angles.

Examples of  supplementary angle

If angle one is equal to 110° and angle two is equal to 70°. State whether they are supplementary or complementary angles.

Angle 1 + Angle 2 = 180°

110° +70°= 180°

Therefore, they are a supplementary angle.

Example 1. Measure angle ABC is 120 °. Find the supplement of another angle. 

                  The measure of supplementary angle is 180° so

                  120° + x = 180°

                   x = 180° -120°

                   x= 60°

Example 2:  Two angles are supplementary if one of the angles is 81°. Calculate and find the measurement of the other angle?

Let the size of the angle be ‘x’ degree. 

Since both the angles are supplementary angles where total will be equal to 180° 

x + 81° = 180°

x = 180° -81°

x= 99° 

Therefore, the size of the other angle is 99°

Example 3: Two angles are supplementary if one of the angles is twice the other angle. What are the sizes of both angles?

Let the one angle be x degree 

The other angle will be 2x degree

As it is supplementary angle the sum of measure of both the angles will be 180°

x + 2x = 180°

3x = 180°

x = 180° divtopicIded by 3 

x= 60°

If one angle is 60° then we can put the value to find the measure of another angle.

2x = 2 * 60 

     = 120°

Therefore one angle is 60° and another angle is 120°

Types of supplementary angle

There are two types of supplementary angles 1) adjacent supplementary angles 2) non-adjacent supplementary angles.

When supplementary angles have a common arm and a common vertex between two angles, they are called adjacent supplementary angles. It shares a common line segment and vertex with each other.

When supplementary angles do not have a common arm and common vertex between two angles, they are known as non-adjacent supplementary angles. They do not share the line segment or the vertex with each other.

Features of supplementary angle: 

Supplementary angles form a straight angle.

Two right angles can form supplementary angles.

One obtuse angle and one acute angle can form a supplementary angle.

They also formed a linear pair of angles. 

Supplemental angles need not be on the same line; they may be on other lines but their sum must measure 180 degrees.

The total of two consecutive angles, created by a ray, standing on the line is 180°.