What are Complementary Angles? Explanation and Examples

The word “complementary” comes from two Latin words, “Complere” and “Plere.” Here “Complere” means “complete,” and “Plere” means “fill.” Thus, complementary angles are a pair of angles that sum up to 90 degrees, forming a right angle. The actual meaning of complimentary is combining objects or things in such a way that they enlarge or enhance the qualities of each other or another.

You can see a lot of real-life examples of complementary angles. For example, when you cut a square cheese slice diagonally, it is divided into two pieces, and two right angles are formed, thus making a pair of complementary angles. Complementary angles can be understood better with the help of real-life examples. Cuemath is an online learning platform that helps students understand the concept of complementary angles with the help of real-life examples.

Defining Complementary Angles

Before understanding what a complementary angle is, let us go through the definition of an angle. An angle is a figure formed by two rays which are also the sides of an angle. These rays share a common endpoint which is known as the vertex where the angle is formed.

Now, what exactly are complementary angles?

When two angles sum up to measure 90 degrees, they are called Complementary Angles. They are composed of two acute angles measuring less than 90 degrees. When complementary angles are put together, they form a right angle that sums up to

90 degrees. Notice that together they make a right angle.

Now that we know what a complementary angle is let us understand the different types of complementary angles.

Types of Complementary Angles

Following are the two types of complementary angles :

Adjacent Complementary Angles: Two complementary angles which have a common vertex and a common arm are called adjacent complementary angles.

Non-adjacent Complementary Angles: Two complementary angles that are not adjacent to each other are called non-adjacent complementary angles.

Here’s a magic rule to find the complementary angle!

To find the complementary angle of a specific angle, you need to subtract the measure of that angle from 90°.

So, the complementary angle = 90° – the given respective angle.

Now, wasn’t that easy? Now let us explore some of the properties of complementary angles.

Characteristics of Complementary Angles

We have now mastered the concept of complementary angles. Now let us look at some important characteristics and features of complementary angles :

  • When two angles are added up to 90 degrees, they are known as Complementary Angles.
  • There are two types of Complementary Angles: Adjacent and nonadjacent Angles.
  • Three or more than two angles cannot be complementary even if their sum is 90 degrees.
  • Two acute angles of a right-angled triangle are complementary in nature.
  • The Greeks found complementary angles.
  • Complementary Angles are vital because they can be used to find out other angles.
  • Two right angles can’t complement each other.
  • Two obtuse angles can’t complement each other.
  • Two complementary angles are acute, but vice versa is not possible or acceptable.

I hope you enjoyed exploring complementary angles with the help of this blog. Complementary angles are an important part of geometry. Complementary and supplementary angles are used to find the missing angles in a sum. They are complete opposites of each other. Complementary Angles should always have positive measures. Negative measures are not accepted in Complementary Angles.

Do not forget to practice sums related to complementary angles regularly!