1. Angles and Diagonals in Polygons

2. The interior angles are the angles inside the polygon. The sum of the interior angles is found when you add up all the angles inside a polygon.

3. On a separate piece of paper: Fill in the rest of the table: ShapeNumber of Sides Sum of Interior Angles Number of Diagonals Triangle3 0 Quadrilateral360 Pentagon 5405 Hexagon6720 Heptagon790014 Octagon

4. 1) What are the patterns that you notice in the sum of interior angles? 2) What are the patterns that you notice in the number of diagonals?

5. Formula to find Sum of Interior Angles Sum = 180(n – 2), when n is the number of sides. For example: Triangle = 3 sides = 180(n – 2) = 180(3 – 2) = 180(1) = 180

6. Formula to find the number of diagonals in a polygon: When n = number of sides in the polygon For example in a hexagon:

7. On the same paper as before, answer the following: 1)What is the sum of interior angles of a polygon with ten sides? 2)What is the sum of interior angles of a polygon with fifteen sides? 3)What is the sum of interior angles of a polygon with 20 sides? 4)How many diagonals are in a shape with eleven sides? 5)How many diagonals are in a shape with seventeen sides?