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, $x = 54^\circ$.

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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.