To determine the number of sides of a regular polygon with a given sum of interior angles, we can use the formula for the sum of the interior angles of an \(\(n\)\)-sided polygon. The formula is given by:
\(\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]\)
We know that the sum of the interior angles is \(\(2,520^\circ\)\). So, we can set up the equation:
\(\[ (n - 2) \times 180 = 2520 \]\)
To solve for \(\(n\)\), follow these steps:
1. Isolate the term involving \(\(n\)\):
\(\[ n - 2 = \frac{2520}{180} \]\)
2. Calculate the right-hand side:
\(\[ \frac{2520}{180} = 14 \]\)
Therefore, we have:
\(\[ n - 2 = 14 \]\)
3. Solve for \(\(n\)\):
\(\[ n = 14 + 2 \]\)
\(\[ n = 16 \]\)
So, the polygon has \(\(16\)\) sides.
