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In the provided triangle, we have an isosceles triangle \( \triangle ABC \), where two sides are equal (denoted by the markings on sides \( AB \) and \( AC \)). The angle at vertex \( C \) is given as \( 72^\circ \).

### Steps to find \( x \):
1. Since \( \triangle ABC \) is isosceles, angles \( A \) and \( B \) are equal, meaning \( \angle A = \angle B = x \).
2. The sum of the angles in any triangle is always \( 180^\circ \). Therefore, we can set up the equation:
   \[
   x + x + 72^\circ = 180^\circ
   \]
   Simplifying:
   \[
   2x + 72^\circ = 180^\circ
   \]
   \[
   2x = 180^\circ - 72^\circ
   \]
   \[
   2x = 108^\circ
   \]
   \[
   x = \frac{108^\circ}{2}
   \]
   \[
   x = 54^\circ
   \]

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

Let me know if you'd like more details or have any other questions!

### 5 Related Questions:
1. What is the sum of the interior angles in any triangle?
2. How can you identify an isosceles triangle based on its sides?
3. What are the properties of isosceles triangles related to their angles?
4. How would you solve this problem if the triangle were not isosceles?
5. How can you use the exterior angle theorem in triangles?

### Tip:
Always remember that in isosceles triangles, the base angles (the two angles opposite the equal sides) are always congruent.

Find the value of x in the isosceles triangle where the angles are 72°, x°, and x°.

Learn how to find the value of x in an isosceles triangle where the given angle is 72°. This problem involves geometric concepts such as the sum of angles in a triangle and properties of isosceles triangles. Suitable for students in Grades 6-8.

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