Question

The sum of the interior angles of a regular polygon is 2340 degrees, How many sides does the polygon have?

Answer 1

360/15 = 24

180 - 24 = 156

156 * 15 = 2340

Therefore 15 sides

Answer 2

I'm not sure if there is a more direct method for it, but basically, I used trial and error for it.

First, I guessed how many sides it might have. I used numbers ranging from 13 to 17 and followed the procedure you see above.

Second, I divided 360 by the number of sides to find the exterior angle.

Third, I subtracted the exterior angle from 180 to find the interior angle.

Finally, I multiplied the interior angle by the number of sides to find the sum of the interior angles.