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.