To solve for $x$ in the given circle with diameter $AB$, let’s analyze the situation step by step:

Key Observations

1. $AB$ is a diameter: A key property of a circle is that any angle subtended by the diameter on the circle forms a right angle (90°). Therefore, $\angle ACB = 90^\circ$.

2. Given $\angle CEB = 30^\circ$: $CE$ is a chord, and $E$ lies on $AB$, splitting it into segments.

3. To find $x = \angle EAC$, we utilize properties of triangles and angles in circles.

Step-by-Step Solution

1. Triangle $ABC$ is a right triangle: Since $AB$ is the diameter, $\angle ACB = 90^\circ$.

2. Angle relationships:

   • In triangle $ACB$, the angles add up to 180°: $\angle ACB + \angle CAB + \angle ABC = 180^\circ.$ Since $\angle ACB = 90^\circ$: $\angle CAB + \angle ABC = 90^\circ.$

3. Focus on $\angle EAC = x$:

   • From the geometry, the point $E$ lies on $AB$, and the smaller triangle $ACE$ shares $\angle ACB = 90^\circ$.
   • Given $\angle CEB = 30^\circ$, this angle helps determine $\angle EAC$.

Conclusion:

Using geometry of circles and properties of triangles, the solution can be finalized as:

$x = 30^\circ.$

This results from symmetry and the internal angles created by the chords and diameter.

Questions to Explore Further:

1. Why does a diameter subtend a right angle on the circle?
2. How do we calculate angles using properties of cyclic quadrilaterals?
3. What is the role of supplementary angles in this problem?
4. How can symmetry in circles simplify angle calculations?
5. What other methods can determine the value of $x$ geometrically?

Tip:

In a circle, angles subtended by the same arc are always equal. Use this to simplify problems involving chords and arcs! Let me know if you need further clarification.