Question

The sum of the interior angles of a regular polygone is 2,340 degree how many sides has it

Answer 1

To find the number of sides in a regular polygon based on the sum of its interior angles, you can use the formula for the sum of the interior angles of a polygon:

\[
S = (n - 2) \times 180
\]

where \( S \) is the sum of the interior angles and \( n \) is the number of sides.

Given that the sum of the interior angles is \( S = 2340 \) degrees, we can set up the equation:

\[
2340 = (n - 2) \times 180
\]

Now, we can solve for \( n \):

1. Divide both sides by 180:

\[
\frac{2340}{180} = n - 2
\]

2. Calculate \( \frac{2340}{180} \):

\[
\frac{2340}{180} = 13
\]

So we have:

\[
13 = n - 2
\]

3. Add 2 to both sides to find \( n \):

\[
n = 13 + 2 = 15
\]

Thus, the polygon has \( \boxed{15} \) sides.