Solving geometry problems with angle equations on a worksheet.

It looks like you've uploaded a worksheet with geometry problems involving angles and algebraic expressions. Based on the visible content, here's a breakdown of what’s happening in the image and how to solve one of the problems (e.g., Problem 5) step-by-step.

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🔍 Problem 5:

Given:
- Two parallel lines cut by a transversal.
- Angles labeled as:
- One angle: \(8x + 17\)
- Another angle: \(3x + 56\)
- The two angles are corresponding angles, so they are equal.

> Note: The teacher has written “Converse: Corresponding ∠s” — meaning we're using the converse of the corresponding angles postulate: if corresponding angles are congruent, then the lines are parallel.

But here, the goal is likely to solve for x using the fact that these angles are equal.

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✔ Step-by-Step Solution:

We are told the angles are corresponding, so:

\[
8x + 17 = 3x + 56
\]

Now solve for \(x\):

1. Subtract \(3x\) from both sides:
\[
8x - 3x + 17 = 56
\]
\[
5x + 17 = 56
\]

2. Subtract 17 from both sides:
\[
5x = 56 - 17
\]
\[
5x = 39
\]

3. Divide both sides by 5:
\[
x = \frac{39}{5} = 7.8
\]

✔ So, \(x = 7.8\)

Then plug back into either expression to find the angle measure:
- \(8x + 17 = 8(7.8) + 17 = 62.4 + 17 = 79.4^\circ\)

So, each angle is approximately \(79.4^\circ\).

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📝 Final Answer for Problem 5:

\[
x = 7.8
\]

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🔁 Converse Statement:

Since the corresponding angles are equal, the lines are parallel.
So, the converse is:
👉 *If corresponding angles are congruent, then the lines are parallel.*

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Let me know which problem you'd like explained next (e.g., #6, #7, etc.), or if you want help with all of them!