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 polygon shown in the diagram has 4 equal sides and 4 equal angles, making it a regular quadrilateral (a square).

$$ n = 4 $$

Calculate the interior angle of the regular polygon

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

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

Substitute \(n = 4\):

$$ x = \frac{(4 - 2) \times 180^\circ}{4} = \frac{2 \times 180^\circ}{4} = 90^\circ $$

Answer:

What is the value of \(x\)?

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

\(x =\) <blank>90</blank>\(^\circ\)