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I see that you've uploaded a math worksheet. I'll help you with the problems that I can see.

Let's go over each problem visible in the image:

### Problem 4:
- You're asked to write an equation and solve for \( x \) to find \( m\angle A \).

The diagram shows two intersecting lines with angle measures given as expressions involving \( x \) (i.e. \( 8x + 10^\circ \) and \( 80^\circ + 4x \)).

Using the fact that vertically opposite angles are equal, you can set up the equation:
\[
8x + 10 = 80 + 4x
\]
Simplifying:
\[
8x - 4x = 80 - 10
\]
\[
4x = 70
\]
\[
x = \frac{70}{4} = 17.5
\]
Now substitute \( x = 17.5 \) into one of the expressions (e.g., \( 8x + 10 \)) to find \( m\angle A \):
\[
m\angle A = 8(17.5) + 10 = 140 + 10 = 150^\circ
\]

### Problem 5a:
- You're asked about the relationship between \( \angle KGF \) and \( \angle FGH \). The diagram seems to indicate that these two angles are equal, likely because they are marked as such. Your solution states that they are both 96°, so that should be correct assuming it follows from the diagram.

### Problem 5b:
- You need to write an equation and solve for \( x \). Without seeing the diagram clearly, it’s hard to interpret the exact equation needed, but based on typical problems of this type, you likely need to use the properties of supplementary or vertical angles to set up an equation.

### Problem 6:
- For each figure, you are asked to write the angle relationship between the given angles:
    - In part (a), you have written "vertical," which is correct if the angles are vertically opposite.
    - In part (b), it seems like you've written "corresponding angles," which may also be correct depending on the diagram.
    - In part (c), it appears that "alternate exterior angles" is what you've written, which would be correct if the angles are on opposite sides of the transversal and outside the parallel lines.

Do you want further clarifications or details on any part of the solution? 

Here are some related questions to deepen your understanding:
1. How can you prove that vertically opposite angles are always equal?
2. What is the difference between corresponding angles and alternate interior angles?
3. Can two adjacent angles be congruent? If so, in what specific cases?
4. What are supplementary angles, and when do they occur in geometric figures?
5. How do parallel lines affect the relationships between angles formed by a transversal?

### Tip:
When solving for unknown angles, always check if the angles are complementary (sum to 90°), supplementary (sum to 180°), or if they are equal due to symmetry, like in vertically opposite angles or angles in isosceles triangles.

The user submitted a math worksheet containing several problems related to angles and algebraic equations. The questions involved solving for unknown angles using properties of vertically opposite angles, supplementary angles, and angle relationships such as corresponding and alternate exterior angles.

Explore how to solve algebraic equations related to angle relationships. Problems include vertically opposite angles, corresponding angles, and alternate exterior angles, suitable for Grades 8-10. Learn to set up and solve equations like 8x + 10 = 80 + 4x and understand key geometric theorems.

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