https://file.aiquickdraw.com/mathbot/file/1726533035111rxlpgfra.jpg

The question asks you to find the missing angles in the diagram, and you’ve already filled in a few, such as \(128^\circ\) and \(136^\circ\). Based on the image, we can analyze the relationships between angles to fill in the missing values.

Here’s how you can approach it:

### 1. **Use of Linear Pair**:
When two angles form a straight line, they add up to 180° (linear pair). For example:
- Angle 1 and Angle 2 are linear pairs.
- Angle 3 and Angle 4 are linear pairs.

### 2. **Use of Vertical Angles**:
Vertical angles are equal. For example:
- Angle 1 and Angle 4 are vertical angles, so they are equal.
- Angle 2 and Angle 3 are vertical angles, so they are equal.

### 3. **Step-by-Step Explanation for Some Angles**:
- Angle 1 is given as \(52^\circ\). Since Angle 1 and Angle 2 are a linear pair, \( \text{Angle 2} = 180^\circ - 52^\circ = 128^\circ \).
- Similarly, Angle 4 is a vertical angle with Angle 1, so \( \text{Angle 4} = 52^\circ \).
- Angle 2 and Angle 3 are vertical angles, so \( \text{Angle 3} = 128^\circ \).
- Angle 5 and Angle 6 are a linear pair. Since Angle 6 is given as \(44^\circ\), \( \text{Angle 5} = 180^\circ - 44^\circ = 136^\circ \).

Now let's fill in the remaining angles:

### 4. **Filling in the Remaining Angles**:
- Angle 7 is vertical to Angle 6, so \( \text{Angle 7} = 44^\circ \).
- Angle 8 is vertical to Angle 5, so \( \text{Angle 8} = 136^\circ \).
- Angle 9 is vertical to Angle 4, so \( \text{Angle 9} = 52^\circ \).
- Angle 10 is vertical to Angle 3, so \( \text{Angle 10} = 128^\circ \).
  
By following the same logic with linear pairs and vertical angles, you can continue filling the rest of the angles on the diagram. Do you want me to go through each remaining angle and fill them in for you?

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Let me know if you'd like further clarification! Here are some follow-up questions to expand this:

1. How do linear pairs and vertical angles relate in geometry?
2. Can you explain how to calculate angles on a straight line?
3. What is the definition of complementary and supplementary angles?
4. How can angles formed by parallel lines and a transversal be calculated?
5. How does the angle sum of a triangle relate to finding missing angles?

**Tip**: Always check for straight lines or intersecting lines to find linear pairs and vertical angles, which makes solving such problems easier.

Find the measures of the missing angles in the diagram, where two angles are already provided: 128° and 136°.

Learn how to find missing angles in a geometry problem by applying the concepts of linear pairs and vertical angles. This problem covers angles on a straight line and vertical angle relationships, suitable for students in Grades 7-9.

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