Find the missing angle measurement using the angle addition postulate

Today you’re going to learn all about angles, more specifically the angle addition postulate.

Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)

We’re going to review the basics of angles, and then use that knowledge to find missing angles with our new postulates.

Let’s dive in!

How To Name An Angle?

The first thing you need to know about angles is how to identify or name them.

For example, did you know that an angle is formed by two rays that have the same common endpoint or initial point?

And that the common endpoint is called the vertex of the angle.

Parts of an Angle

To name the angle we typically use three points when naming an angle, one point on each side and also the vertex. It is important to note that the vertex must always be the middle letter.

The angle seen below can be named ∠NPM or ∠MPN

Naming an Angle

Angle Classifications

And angles are classified as to their measure and are labeled as either acute angles, right angles, obtuse angles, or straight angles.

Angle Classification

Did you know that there is something amazing about adjacent angles?

First, adjacent angles are two angles that have a common vertex and side but no common interior points. Meaning, they are two angles side-by-side with the same vertex.

Adjacent Angles Examples

But the most significant thing about adjacent angles is that we can add their measures to create larger angles.

How?

By using the Angle Addition Postulate!

Definition

The postulate states that if we have two adjacent angles, we can add their measures to help us find unknown angles.

Angle Addition Postulate Definition

Example

As seen in the example to the right, ∠ACB + ∠CDB = ∠ADC

Angle Addition Postulate Example

And finally, just like we saw with segments, angles also have bisectors.

We discuss this in detail in the video below, but essentially an angle bisector is a ray from the vertex of an angle that forms two congruent angles from the given angle.

In other words, it divides the angle in half, or cuts it into two equal parts, as Math is Fun accurately states.

Angle Bisector

Together we will learn how to:

• Identify and classify angles.
• Understand adjacent angles.
• Use the angle addition postulate to find angle measures.
• Recognize an angle bisector.
• Identify congruent angles.

Angles and Their Measures – Lesson & Examples (Video)

1 hr 0 min

• Introduction to angles.
• 00:00:16 – What is an angle?
• 00:07:28 – Understanding adjacent angles and how to classify angles (Examples #1-4)
• 00:16:34 – What is the angle addition postulate (Examples #5-7)
• Exclusive Content for Member’s Only

• 00:28:11 – Find the measure of each angle and classify the angle (Examples #8-20)
• 00:39:53 – What is an angle bisector? (Examples #21-23)
• 00:45:32 – Find the measure of each angle given an angle bisector (Examples #24-25)
• 00:53:29 – Tell whether each statement is always, sometimes or never true (Examples #26-30)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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