What are Complementary Angles? How to Figure Out Complementary and Supplementary Angles?


Calculating the degrees of angles is a foundational concept in geometry and trigonometry. This vital knowledge is also helpful in field of architecture, engineering, astronomy, etc. Having this important skill enables students to identify both supplementary and complementary angles. It is also necessary in learning more advanced concepts, like radians, sector area, arc length, etc. Concept of supplementary and complementary angles promotes the understanding of describing the relationship between two angles.

Based on the grades and the math level of each student they have to master this necessary skill of identifying degrees of angles and their types using different methods. When any two angles are complementary, the sum of their degrees is 90 degrees. The sum of two supplementary angles add up to 180 degrees or a straight line and is also known as the angles on a straight line. With the knowledge of identifying one of these angles, students can use the complementary or supplementary relationship to calculate the measurement of the other angle.

Definition of Complementary Angles

Two angles are complementary to each other if the sum of their degrees adds up to 90 degrees. In other words, when complementary angles are summed up together, they form a right angle. Therefore, if angle one and angle two are complementary to each other, their sum will be equal to 90 degrees. 
∠1 +∠2 = 90°, where angle -1 and angle-2 are called complements angles.

Finding Complement of an Angle

Complement means to add up to something to make it a whole. In terms of geometry, the sum of two complementary angles always add up to 90°. Finding the complement of an angle simply means to identify the degree of the other angle by using the value of given angle. As we already know the sum of two complementary angles is 90 degrees, we can simply subtract its value to find the complement of this angle. For instance, the complement of an angle of x° is 90 minus x°.
Example: Let’s learn to find the complement of the angle of 49°. 
The complement of 49° can be obtained by subtracting it from 90°. That is 90° – 49° = 41°. Thus, the complement of 49° angle is 41°.

Properties of Complementary Angles

Since we already know about the types of complementary angles. Let’s have a look at some important properties of complementary angles. The properties of complementary angles are given below.

  • Two angles are said to be complementary if they add up to 90 degrees.
  • Two complementary angles can be either adjacent or non-adjacent.
  • Three or more angles cannot be complementary even if their sum is 90 degrees.
  • If two angles are complementary, each angle is called “complement” or “complement angle” of the other angle.
  • Two acute angles of a right-angled triangle are complementary.

Differentiating Between Supplementary and Complementary Angles:

The supplementary and complementary angles are angles that exist in pairs, summing up to 180 and 90 degrees, and have numerous real-time applications, most common being the crossroads. Let’s have a look at the difference between them.

  • A pair of angle are said to be supplementary if their sum is 180 degrees. A pair of angle are said to be complementary if their sum is 90 degrees.
  • Supplement of an angle x° is (180 – x)°. The complement of an angle x° is (90 – x)°

Here is a short trick for you to understand the difference between supplementary angles and complementary angles.
“S” is for “Supplementary” and “S” is for “Straight.” Hence, you can remember that two “Supplementary” angles when put together form a “Straight” angle. “C” is for “Complementary” and “C” is for “Corner.” Hence, you can remember that two “Complementary” angles when put together form a “Corner (right)” angle.