Home » Math Theory » Geometry » Adding and Subtracting Angles

After reading this article, you will be able to add and subtract angles in a given figure or problem. You will also be able to define an angle and know the importance of adding and subtracting angles.

## What is an angle?

A figure produced by two rays meeting at a common terminal point is known as an angle. An angle is denoted by the symbol and is usually measured in degrees.

Angles are sections of a full circle. A full circle can be divided into angles of many sizes. If all of the angles are placed together without overlapping, their total will be 360°. Angles can be added together to make larger angles and can also be divided into smaller angles.

Two angles that are next to each other without overlapping are called adjacent angles. These angles can be added together to make a larger angle. Adding angles is the same as adding numbers. We can add two or more angles as long as they are not overlapping.

Example #1

MON and NOP are two adjacent angles. What is the total angle measure of the two angles?

Solution

Example #2

If BAC and CAD are two adjacent angles, determine their angle measure if we add them together.

Solution

Example #3

WXZ and ZXY are two adjacent angles. What is the sum of the two adjacent angles?

Solution

Example #4

MJK and KJL are two adjacent angles. Find the sum of the two angles.

Solution

## How to subtract angles?

If a large angle is made up of two smaller angles, the measurement of one of the smaller angles can be subtracted from the measurement of the large angle to find the measurement of the second small angle. Just like the addition of angles, subtraction of angles is the same as simply subtracting numbers.

Example #1

If ABD measures 136°, what is the measure of ABC?

Solution

Example #2

Based on the figure, if RUP measures 225°, what is the measure of QUP?

Solution

## How to solve problems involving addition and subtraction of angles?

When solving problems involving addition and subtraction of angles, we must first be able to define what angles make up the larger angle. That way, we can avoid confusion.

Example

Angle MOP measures 126°. It is divided into two smaller angles namely, Angle MON and Angle NOP. Angle MON measures 58°, while angle NOP is unknown.

If Angle MON + Angle NOP = Angle MOP, what is the measure of Angle NOP?

Solution

## What is the importance of adding and subtracting angles?

One of the significance of adding and subtracting angles is that it allows us to create larger angles. More so, it helps us prepare when it comes to the pairs of angles such as supplementary and complementary angles. Adding and subtracting angles can also help us in proving certain theorems and congruent triangles.