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

1 answer

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:

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

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

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

So we have:

\[ 13 = n - 2 \]

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

\[ n = 13 + 2 = 15 \]

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