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We are given a triangle inscribed in a circle, with \( AC = BC \) (i.e., triangle \( ABC \) is isosceles), and \( \angle ABC = 72^\circ \). We are tasked with finding \( x \), which represents \( \angle ACB \).

### Steps to Solve:

1. Since \( AC = BC \), triangle \( ABC \) is isosceles, so \( \angle BAC = \angle ACB = x \).

2. The sum of the angles in any triangle must equal \( 180^\circ \). Therefore, in triangle \( ABC \):

\[
\angle ABC + \angle BAC + \angle ACB = 180^\circ
\]

Substitute the given angle and the unknowns:

\[
72^\circ + x + x = 180^\circ
\]

3. Simplifying the equation:

\[
72^\circ + 2x = 180^\circ
\]

\[
2x = 180^\circ - 72^\circ = 108^\circ
\]

\[
x = \frac{108^\circ}{2} = 54^\circ
\]

Thus, \( x = 54^\circ \).

### Conclusion:
The measure of \( \angle ACB \) is \( 54^\circ \).

Do you have any questions or would you like a further explanation?

Here are five related questions:
1. How do we calculate the angles in any triangle?
2. What are the properties of an isosceles triangle?
3. How do we use the sum of angles in a triangle to solve for unknowns?
4. What are the rules for angles in a cyclic quadrilateral?
5. How do we use geometric theorems to solve problems involving circles?

**Tip:** When solving problems involving isosceles triangles, remember that two angles are equal, which simplifies finding unknown angles.

Learn how to find the unknown angle x in an isosceles triangle inscribed in a circle, where AC = BC and ∠ABC = 72°. This problem uses key concepts from geometry, including isosceles triangles and the sum of angles in a triangle.

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