To solve for $x$, we need to analyze the relationships between the angles in the given diagram.

1. Identify angle relationships: The diagram shows several parallel and intersecting lines, labeled with various angles:

   • Line $a \parallel d$, and $b$ is a transversal.
   • The angles around points $A$, $B$, $E$, and $D$ relate due to properties of parallel lines and transversals.

2. Using Corresponding Angles:

   • Since $a \parallel d$ and $b$ is a transversal, the angle at $B$ (57°) is equal to angle $E$, as they are corresponding angles. So: $\angle E = 57^\circ$

3. Determine Angle $x$:

   • Angle $x$ and the 57° angle (which we identified as $\angle E$) are on a straight line, making them supplementary.
   • Therefore: $x + 57^\circ = 180^\circ$
   • Solving for $x$: $x = 180^\circ - 57^\circ = 123^\circ$

So, the value of $x$ is $\mathbf{123^\circ}$.

Would you like more details or have any questions?

Related Questions:

1. What are corresponding angles, and why are they equal when lines are parallel?
2. How would you solve for unknown angles if more angles were missing?
3. What other properties of angles can help solve complex diagrams like this?
4. How do supplementary angles relate to parallel lines?
5. What would change if the lines were not parallel?

Tip:

When working with parallel lines, remember that corresponding, alternate interior, and alternate exterior angles are equal.