Angle Addition Postulate practice worksheet with six problems and diagrams.

It looks like you've uploaded an image containing a worksheet titled "ANGLE ADDITION POSTULATE - Practice", which includes several geometry problems involving the Angle Addition Postulate.

Since I can't view images directly, I'll explain how to solve such problems and provide a general guide based on what's typically found in these types of worksheets. If you can describe the specific problems or provide the text from the image, I can give more precise solutions.

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🔍 What is the Angle Addition Postulate?

The Angle Addition Postulate states:

> If point $ B $ lies in the interior of $ \angle AOC $, then
> $$
> \angle AOB + \angle BOC = \angle AOC
> $$

This means that if you have two adjacent angles that form a larger angle, the sum of the measures of the smaller angles equals the measure of the larger angle.

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🧩 Common Problem Types on This Worksheet

Here are typical problems found in such worksheets:

#### Example 1: Find the measure of a missing angle
Given:
- $ \angle ABC = 90^\circ $
- $ \angle ABD = 35^\circ $

Find $ \angle DBC $.

Solution:
$$
\angle DBC = \angle ABC - \angle ABD = 90^\circ - 35^\circ = 55^\circ
$$

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#### Example 2: Use algebra with the postulate
Given:
- $ \angle MNO = 120^\circ $
- $ \angle MNP = 2x + 10 $
- $ \angle PNO = x + 20 $

Find $ x $ and the measures of each angle.

Solution:
Use the Angle Addition Postulate:
$$
\angle MNP + \angle PNO = \angle MNO
$$
$$
(2x + 10) + (x + 20) = 120
$$
$$
3x + 30 = 120
$$
$$
3x = 90 \Rightarrow x = 30
$$

Now substitute:
- $ \angle MNP = 2(30) + 10 = 70^\circ $
- $ \angle PNO = 30 + 20 = 50^\circ $

Check: $ 70 + 50 = 120^\circ $ ✔

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#### Example 3: Find total angle measure
Given:
- $ \angle XYZ $ is split into $ \angle XYW = 45^\circ $ and $ \angle WYZ = 65^\circ $

Find $ \angle XYZ $.

Solution:
$$
\angle XYZ = 45^\circ + 65^\circ = 110^\circ
$$

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✔ Tips for Solving These Problems

1. Identify the full angle and its parts.
2. Label known angles and variables.
3. Apply the Angle Addition Postulate:
$$
\text{Part} + \text{Part} = \text{Whole}
$$
4. Solve equations if variables are involved.
5. Double-check that your answer makes sense geometrically.

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📝 How You Can Help Me Solve Your Specific Problems

Please describe or type out the problems from the image. For example:

> "Problem 1: In the diagram, $ \angle ABC = 100^\circ $. Point D lies inside $ \angle ABC $, and $ \angle ABD = 40^\circ $. Find $ \angle DBC $."

Then I’ll walk you through the solution step by step.

Alternatively, if you can copy and paste the text from the image, I’ll solve all the problems for you!

Let me know!