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