Triangle+Polygons

**Divide Regular Polygons into Triangles by connecting one vertex to all of the others.** **A Pentagon has 5 sides and we made 3 triangles.** A Hexagon has 6 sides and we made 4 triangles. **A Polygon with n sides will make (n - 2) triangles.**
 * Regular Polygons** __**Interior Angles**__
 * A Square has 4 sides and we made 2 triangles.**

**With the Square, we made 2 Triangles. All of the interior angles of the 2 Triangles make up the interior angles of the Square.**

**The sum of the 2 Triangle's angles is 180 + 180 = 360.**

**A Square has 4 equal angles,**

so 360/4 gives us that the interior angle of a Square is 90.

**With the Pentagon, we made 3 Triangles.** **The sum of the 3 Triangle's angles is 180 + 180 + 180 = 540.**

**A Pentagon has 5 equal angles, so 540/5 gives us that the interior angle of a Pentagon = 108.**

**With the Hexagon, we made 4 Triangles.**


 * The sum of the 4 Triangle's angles is 180 + 180 + 180 + 180 = 720.**


 * A Hexagon has 6 equal angles, so 720/6 gives us that the interior angle of a Hexagon = 120.**

**How about a 100-gon? (That's a regular polygon with 100 sides.) There would be 98 triangles...**



**In general, the measure of an interior angle of a regular n-gon is**



Website []

The exterior angle is equal = 360/n where n is the number of sides. The interior angle can also be found by 180 - exterior angle.
 * __Exterior Angles__**