The problem involves a regular polygon, and the goal is to find the value of $x$, which likely corresponds to an angle related to the interior or exterior angles of the polygon.

Key Steps to Solve:

1. Understanding the Regular Polygon:

   • The sum of the interior angles of a polygon with $n$ sides is given by: $\text{Sum of Interior Angles} = 180(n - 2)$
   • Each interior angle of a regular polygon is: $\text{Interior Angle} = \frac{180(n - 2)}{n}$
   • Each exterior angle of a regular polygon is: $\text{Exterior Angle} = \frac{360}{n}$

2. Given Information:

   • The diagram shows an angle $x$, which might be either an interior or exterior angle of the polygon.
   • The triangle in the diagram suggests $x$ is related to either an interior or exterior angle.

3. Solution: Let me examine the triangle shown more closely. Based on the provided angle, I will calculate $x$ using the regular polygon formula.

I’ll now analyze the triangle and calculate accordingly.From the provided image, the triangle suggests that $x$ represents an interior angle of a regular polygon. Here’s how to calculate:

Steps to Determine $x$:

1. Determine the Relationship: In a regular polygon, each interior angle $x$ can be calculated using the formula: $\text{Interior Angle} = \frac{180(n - 2)}{n}$ where $n$ is the number of sides of the polygon.

2. Analyze the Polygon:

   • From the diagram, the triangle seems part of the polygon, and $x$ is likely one of the interior angles of the polygon.
   • We would need additional details (such as $n$) to calculate the value of $x$. However, since the problem mentions "regular polygon," $x$ corresponds directly to the above formula for the interior angle.

Missing Information:

If $n$ (the number of sides) is available, we can plug it into the formula and calculate $x$. Could you confirm or provide the number of sides of the polygon?