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In the diagram provided, we have two parallel lines \( AB \parallel CD \) and two transversals \( EF \) and \( GH \). The angles formed are labeled as \( 3x + 15^\circ \) at two positions: one at \( \angle G \) and the other at \( \angle H \).

### Step-by-Step Solution:

1. **Identify the corresponding angles:**
   Since \( AB \parallel CD \), the angle \( \angle G \) and \( \angle H \) are corresponding angles, meaning they are equal due to the "Corresponding Angles Postulate" (when two parallel lines are crossed by a transversal, the corresponding angles are equal).

2. **Set up the equation:**
   Since \( \angle G = \angle H \), we can set the expressions for both angles equal:
   \[
   3x + 15^\circ = 3x + 15^\circ
   \]
   This is an identity, meaning the equation is true for all values of \( x \). However, the diagram seems to have an implicit meaning for the sum of angles around point \( G \) or \( H \).

3. **Interpretation via supplementary angles:**
   Based on the visual arrangement, angles \( \angle G \) and \( \angle H \) might also represent a situation where these angles are supplementary. If they are on the same side of the transversal, their sum must be \( 180^\circ \).

4. **Equation with supplementary angles:**
   We can set up the equation assuming \( \angle G \) and \( \angle H \) are supplementary:
   \[
   3x + 15^\circ + 3x + 15^\circ = 180^\circ
   \]
   Simplifying this:
   \[
   6x + 30^\circ = 180^\circ
   \]
   Subtract \( 30^\circ \) from both sides:
   \[
   6x = 150^\circ
   \]
   Divide by 6:
   \[
   x = 25^\circ
   \]

Thus, the value of \( x \) is \( \boxed{25^\circ} \).

Would you like a more detailed breakdown or explanation? Here are 5 related questions to practice:

1. What are corresponding angles, and why are they equal when lines are parallel?
2. If the angles were not corresponding, what other geometric relationships could be applied to solve for \( x \)?
3. How do you determine whether angles are supplementary when transversals intersect parallel lines?
4. Can you apply this reasoning to a similar diagram with different angle expressions?
5. How would the solution change if the angle expression had a different coefficient of \( x \)?

### Tip:
Always identify whether angles are corresponding, alternate, or supplementary when working with parallel lines and transversals. This will guide you in setting up the correct equation.

Find the unknown x in each of the diagrams below. You must provide the reasoning. Lines indicated with arrows are parallel.

This solution explains how to find the unknown angle x in a geometry problem involving parallel lines and transversals. We apply the Corresponding Angles Postulate and the Supplementary Angles Theorem to solve for x. Suitable for students in Grades 8-10.

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