1. Polygon Learning intentions: What is a polygon?
Sum of interior angles in polygons.

2. How can I find angle measures in polygons without using a protractor?

3. Polygon Many angles Poly- means "many" gon means "angle".
Polygon comes from Greek.
Poly- means "many"
gon means "angle".
Many angles

4. A polygon is a Plane shape with straight sides.
What is a polygon?
A polygon is a Plane shape with straight sides.
Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).
Resource:

5. Polygons

6. Nonexamples

7. Types of Polygons http://www.mathsisfun.com/geometry/polygons.html
Regular or Irregular
If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular
Concave or Convex
A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)
Convex
Concave

8. Polygons Can be concave or convex. Concave Convex
The diagonals of the convex
polygon all lie within the
figure.
Non-convex polygons have some diagonals
that do not lie within the figure. Some interior
angles are reflex (greater than 180°).

9. Polygons are named by number of sides
Triangle 3 4
Quadrilateral
Pentagon 5
Hexagon 6
Heptagon 7 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
n-gon

10. Sums of Interior Angles

11. Then draw diagonals to create triangles.
Draw a:
 Quadrilateral  Pentagon
 Hexagon  Heptagon
 Octogon
Then draw diagonals to create triangles.
A diagonal is a segment connecting two nonadjacent vertices (don’t let segments cross)
Add up the angles in all of the triangles in the figure to determine the sum of the angles in the polygon.
Complete this table
Polygon
# of sides
# of triangles
Sum of interior angles

12. Sums of Interior Angles
Triangle
Quadrilateral
Pentagon
= 2 triangles
= 3 triangles
Hexagon
Octagon
= 4 triangles
Heptagon
= 5 triangles
= 6 triangles

13. Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon
Polygon
# of sides
# of triangles
Sum of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon 3 1
180° 4 2
2 x 180 = 360° 5 3
3 x 180 = 540° 4
4 x 180 = 720° 6 7 5
5 x 180 = 900° 8 6
6 x 180 = 1080° n
n - 2
(n – 2) x 180°

14. Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon
Polygon
# of sides
# of triangles
Sum of interior angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon 3 1
180° 4 2
2 x 180 = 360° 5 3
3 x 180 = 540° 4
4 x 180 = 720° 6 7 5
5 x 180 = 900° 8 6
6 x 180 = 1080° n
n - 2
(n – 2) x 180°

15. Find the angle sum of a polygon with 18 sides. Solution
The angle sum of a polygon with n sides is given by:
angle sum = (n − 2) × 180° or 180(n − 2)°
Find the angle sum of a polygon with 18 sides.
Solution
Angle sum = (18 − 2) × 180°
= 16 × 180°
= 2880°
Find the angle sum of a polygon with sides.
Solution
Angle sum = (4 − 2) × 180°
= 2 × 180°
= 360°.

16. End