https://file.aiquickdraw.com/mathbot/file/17263137307772ohii2cv.jpg

In the given figure, lines \( AB \parallel CD \), and we need to find the value of \( x \).

### Analysis:
1. The angles given are:
   - \( \angle ABE = 108^\circ \)
   - \( \angle CED = 95^\circ \)
   - \( \angle BAE = 3x + 15^\circ \)

2. Since \( AB \parallel CD \), \( \angle ABE \) and \( \angle CED \) are consecutive interior angles, meaning they add up to \( 180^\circ \) because of the parallel lines.

   So:
   \[
   108^\circ + (3x + 15^\circ) = 180^\circ
   \]

### Solving for \( x \):
\[
108 + 3x + 15 = 180
\]
\[
123 + 3x = 180
\]
\[
3x = 180 - 123
\]
\[
3x = 57
\]
\[
x = \frac{57}{3} = 19
\]

Thus, the value of \( x \) is **19**.

Would you like more details on any step or further explanation?

### Related Questions:
1. What is the property of consecutive interior angles?
2. How do parallel lines affect the angles formed by a transversal?
3. Can you prove the sum of angles in a straight line?
4. What is the relationship between alternate interior angles?
5. How does the exterior angle theorem apply to this figure?

### Tip:
Always double-check angle relationships in geometry problems involving parallel lines, as they often hold key information.

In the given figure AB || CD, find the value of x.

Solve a geometry problem where AB is parallel to CD. Learn how to apply the Consecutive Interior Angles Theorem and find the value of x. Suitable for students in Grades 8-10.

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