What are Supplementary Angles?
Any two angles are said to be supplementary angles if the sum of the two angles is 180 degrees.
Examples of Supplementary Angles
• Sum of 120 degrees and 60 degrees will be 180 degrees.
• Sum of 50 degrees and 130 degrees will be 180 degrees.
• Sum of 45 degrees and 135 degrees will be 180 degrees.
• Sum of 90 degrees and 90 degrees will be 180 degrees.
All the above examples show that the total of the given two angles is 180 degrees. Hence, these angles are supplementary angles.
Position of the Supplementary Angles
Two Supplementary Angles can be adjacent to each other but it is not compulsory i.e. two Angles supplementary to each other need not lie on the same side and need not be adjacent and can have space in between the two angles.
To understand it better, let us consider a cyclic quadrilateral and a parallelogram. In a cyclic quadrilateral, all the vertices lie on a single circle. In such cases, the opposite angles are supplementary. In case of parallelogram, the angles supplementary to each other lie adjacent to each other. If two angles are formed on the same circle by the tangent lines drawn from an exterior point x, then these two angles are said to be supplementary angles.
How to Solve Supplementary Angles?
Now let us see how to solve supplementary angles. As per the concept of supplementary angles, the sum of the two angles is 180 degrees. If we consider one of the supplementary angle as x degrees, then the other supplementary angle is given by (180 – x).
In notation, we can write, x + (180-x) = 180 degrees. Using this formula, if one supplementary angle (x degrees) is known, then the other supplementary angle can be easily calculated.
For example, consider the mathematical problem mentioned below:
Problem: Given two supplementary angles, out of which one angle is 60 degrees. Find the other angle.
Answer:
From the problem, we know that the value of one supplementary angle is 60 degrees. By assigning the given value to the variable x, we get:
First variable = x = 60
Second Variable = 180 – x = 180 – 60 = 120 degrees.
We can verify it by applying in the formula “x + (180-x) = 180 degrees”. The sum of 60 degrees and 120 degrees gives 180 degrees. The values satisfy the formula and thus it evidently proves that 60, 120 degrees are supplementary angles.
Supplementary angles as Adjacent and Straight Angle
If the two angles supplementary to each other have a common vertex and share the same side, then we can term them as two Adjacent Supplementary Angles. Two Adjacent Supplementary Angles Form a straight angle i.e. 180 degrees. In such cases, we can see that a straight line is formed on the non-shared sides.
