https://file.aiquickdraw.com/mathbot/file/17289093355965rswpmi9.jpg

The polygon in the image is a regular heptagon (7 sides). To calculate the value of \( x \), we need to determine the interior angle of a regular heptagon.

The formula for the interior angle of a regular polygon with \( n \) sides is:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

For a heptagon (\( n = 7 \)):

\[
\text{Interior Angle} = \frac{(7 - 2) \times 180^\circ}{7} = \frac{5 \times 180^\circ}{7} = \frac{900^\circ}{7} \approx 128.6^\circ
\]

Therefore, the value of \( x \) is approximately \( 128.6^\circ \).

Let me know if you need any more details or further explanation!

Here are 5 related questions for further practice:
1. What is the interior angle of a regular octagon (8 sides)?
2. How do you calculate the sum of interior angles of any polygon?
3. What is the exterior angle of a regular heptagon?
4. How does the number of sides affect the size of each interior angle in a polygon?
5. If one of the angles in a regular polygon is \( 135^\circ \), how many sides does the polygon have?

**Tip:** For any regular polygon, the exterior angle is always \( \frac{360^\circ}{n} \), where \( n \) is the number of sides.

The diagram shows a regular polygon. What is the value of x?

This page provides a step-by-step guide to calculate the interior angle of a regular heptagon, using the formula (n - 2) × 180° / n. Perfect for students learning about polygons and angle calculation in Grades 8-10.

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