Polygon Interior Angles Calculation

This problem asks us to determine the number of sides of a polygon given that the sum of its interior angles is \(2160^\circ\). To solve this, we will use the standard formula for the sum of interior angles of any polygon.

Polygon Angle Formula Explained

A polygon is a closed two-dimensional figure with straight sides. The interior angles are the angles formed inside the polygon by its adjacent sides. There is a well-known formula that relates the sum of these interior angles to the number of sides the polygon has.

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

\[ \text{Sum of Interior Angles} = (n - 2) \times 180^\circ \]

Where \(n\) represents the number of sides of the polygon.

Sides Calculation Method

We are given that the sum of the interior angles of the polygon is \(2160^\circ\). We can use this information along with the formula to find the number of sides, \(n\).

• Given: The sum of the interior angles \( = 2160^\circ \)
• Formula to use: \( (n - 2) \times 180^\circ = \text{Sum of Interior Angles} \)

Let's substitute the given sum into the formula:

\[ (n - 2) \times 180^\circ = 2160^\circ \]

To find the value of \(n\), we first need to divide both sides of the equation by \(180^\circ\):

\[ n - 2 = \frac{2160^\circ}{180^\circ} \]

Performing the division:

\[ n - 2 = 12 \]

Now, to isolate \(n\), we add 2 to both sides of the equation:

\[ n = 12 + 2 \]

\[ n = 14 \]

Polygon Sides Result

Based on our calculations, the number of sides of the polygon with an interior angle sum of \(2160^\circ\) is 14. This type of polygon is known as a tetradecagon.