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

The given regular polygon has \(n = 5\) sides (a regular pentagon).

Calculate the interior angle of a regular pentagon

Using the interior angle formula for a regular polygon with \(n\) sides:

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

Substitute \(n = 5\):

$$ x = \frac{(5 - 2) \times 180^\circ}{5} = \frac{3 \times 180^\circ}{5} = 108^\circ $$

Answer:

What is the value of \(x\)?

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

\(x =\) <blank>108</blank>\(^\circ\)