Question

Question was provided via image upload.

Explanation:

Count the number of sides of the regular polygon

By carefully counting the vertices and sides of the regular polygon shown in the diagram:

• There are 9 sides (a regular nonagon).
• Therefore, \(n = 9\).

Apply the interior angle formula

Using the Interior Angle Formula for a regular polygon with \(n\) sides:

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

Calculate the value of the interior angle

Using the Regular Polygon Angles concept, substitute \(n = 9\) into the formula:

$$ \text{Interior Angle} = \frac{(9 - 2) \times 180^\circ}{9} = \frac{7 \times 180^\circ}{9} = 7 \times 20^\circ = 140^\circ $$

Thus, the value of the interior angle \(x\) is \(140\).

Answer:

The diagram shows a regular polygon.

What is the value of \(x\)?

Write your answer as an integer or as a decimal rounded to the nearest tenth.

\(x =\) <blank>140</blank>