This week in foundations 11 i learned how to figure out how many triangles are inside of a specific polygon and how to figure out what the interior and exterior angles are.

To figure out how many triangles are inside of the polygon, you take the number of sides of the polygon and subtract two from that number and that gives you the amount of triangles that are in the polygon. To figure out the sum of the interior angles in the polygon, you take the number of triangles in the polygon and times it by 180. To figure out the size of an interior angle in a  regular polygon, you take the sum of  all the interior angles and divide it by the number of sides on the polygon. To be able to figure out the sum of all exterior angles, you take 360 and divide it by the number of sides.

Example number 1:

Polygon with 5 sides (Pentagon)

5-2=3 the number of triangles in a pentagon is 3.

180 x 3 = 540. 540 is the sum of all interior angles in the pentagon.

540 divided by 5 = 108. 108 is the size of an interior angle in a regular polygon.

180-108=72

72 x 5 (the number of sides)  = 360. 360 is the sum of all exterior angles in the pentagon.

Example number 2:

15 sided polygon

15- 3= 13, 13 triangles in the polygon

180 x 13=2340

2340 divided by 15 = 156

180-156=24

24 x 15 = 360