# Complementary Angles – Meaning, Definition With Examples

Updated on January 3, 2024

Hello, budding mathematicians! Welcome to another exciting journey with us here at Brighterly, your favorite online hub for all things mathematical. Today, we’re diving headfirst into the intricate, fascinating world of geometry, specifically, we’re exploring the concept of Complementary Angles. You might have encountered them before in your math homework, or they might be entirely new to you, but by the end of this article, we promise you’ll know them like the back of your hand. Just like the complementary colors that make your art projects stand out, these angles are all about teamwork and creating something greater together. Let’s discover what happens when two angles come together to perfectly complete a right angle!

## What Are Complementary Angles?

Complementary angles, in their most basic definition, are two angles that together form a right angle. This means their measures add up to 90 degrees. Whether they’re next to each other forming a right angle or positioned apart, as long as their sum totals to 90 degrees, these angles complement each other, hence the name ‘Complementary Angles’.

## Definition of Complementary Angles

Let’s delve a bit deeper into the concept. In the realm of geometry, complementary angles are defined as a pair of angles with the sum of their measures equal to 90 degrees. It’s important to remember that it’s the sum of the measures that matters, not the individual measures themselves.

## Examples of Complementary Angles

The beauty of complementary angles is that they can come in all shapes and sizes! For instance, a 30-degree angle and a 60-degree angle are complementary because when added together, they make a right angle (90 degrees). Even a 45-degree angle and another 45-degree angle are complementary, each contributing equally to form the perfect right angle.

## Properties of Complementary Angles

Some interesting properties about complementary angles are as follows:

- Each angle is called the ‘complement’ of the other.
- If two angles are complementary to the same angle (or congruent angles), then these two angles are congruent.
- If one angle is the complement of the other, they are known as a complementary pair.

## Definition of Complementary Angles in Geometry

In Geometry, complementary angles can be adjacent (next to each other) or non-adjacent. If they’re adjacent, they form a ‘linear pair’ or ‘straight angle’. If they’re not adjacent, they can be anywhere in the plane and still be considered complementary as long as their degrees add up to 90.

## Definition of Complementary Angles in Trigonometry

In the field of Trigonometry, complementary angles have a unique property. The trigonometric function (sine, cosine, tangent, etc.) of an angle is equal to the co-function (cosine, sine, cotangent, etc.) of its complement.

## Difference Between Complementary and Supplementary Angles

While both concepts revolve around the sums of angles, complementary angles add up to 90 degrees, forming a right angle. On the other hand, supplementary angles add up to 180 degrees, forming a straight line.

## Formulas involving Complementary Angles

One can identify complementary angles by using the formula `A + B = 90 degrees`

, where A and B are the measures of two angles. If the sum equals 90 degrees, then A and B are complements of each other.

## Writing Equations involving Complementary Angles

In algebra, complementary angles can be represented as `x`

and `90-x`

. If an angle measures `x`

degrees, its complement is `90-x`

degrees. Together, they add up to form a right angle.

## Practice Problems on Complementary Angles

It’s time for some hands-on practice! Here are a few problems to test your understanding:

- If one angle measures 40 degrees, what is its complement?
- Two angles are complementary. If one angle measures
`x`

degrees, express the other angle in terms of`x`

.

## Conclusion

What an enriching journey it has been exploring Complementary Angles! Here at Brighterly, we pride ourselves in providing fun, easy-to-understand, and comprehensive learning experiences, and we hope this journey into the world of geometry has been just that for you. We explored together, learned together, and we’re sure that you’ve become a mini-expert on complementary angles. As we have seen, these angles are all about the beautiful synergy of numbers and shapes – proof that teamwork truly makes the dream work, even in mathematics. Remember, just like these angles, no matter how small we might be on our own, together we can form something perfect. Keep exploring, keep learning, and remember – mathematics is not just a subject, it’s a way of understanding the world around us. Stay bright with Brighterly!

## Frequently Asked Questions on Complementary Angles

### Are all complementary angles adjacent? Great question!

Complementary angles can indeed be adjacent, which means they’re right next to each other, sharing a common side and a common vertex. When they’re adjacent, they form what’s called a ‘right angle’. But guess what? Complementary angles can also be non-adjacent. This means they can be located anywhere, not necessarily next to each other. The only requirement for two angles to be complementary is that their degree measures add up to exactly 90 degrees.

### What is the complement of a 70-degree angle?

Fantastic! You’re starting to think in terms of complementary angles. Now, let’s remember the main rule: complementary angles add up to 90 degrees. So, if you have an angle that measures 70 degrees, its complement would be the angle that, when added to 70, gives us 90. In this case, that would be 90 – 70, which equals 20 degrees. So, the complement of a 70-degree angle is a 20-degree angle.

### Do complementary angles always form a right angle?

Absolutely! That’s the key definition of complementary angles. Whenever you have two angles and their degree measures add up to 90 degrees, they form a right angle when they’re adjacent. So yes, by definition, the sum of the measures of complementary angles is always 90 degrees, which is precisely the measure of a right angle. This is what makes them so essential in geometry, especially when studying right triangles and trigonometry.