Question

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 = \square^{\circ}\\)

Explanation:

Count the number of sides of the regular polygon

We count the number of sides \(n\) of the regular polygon shown in the diagram:

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

Apply the interior angle formula

The formula for the measure of each interior angle of a regular \(n\)-sided polygon is:

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

Calculate the value of x

Substitute \(n = 9\) into the formula:

$$ x = \frac{(9 - 2) \times 180}{9} $$

$$ x = \frac{7 \times 180}{9} $$

$$ x = 7 \times 20 = 140 $$

Answer:

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>\(^\circ\)