1. Angles of Polygons

2. What does the word “polygon” mean?
Let's Discuss
What does the word “polygon” mean?
What is the smallest number of sides a polygon can have?
What is the largest number of sides a polygon can have?

3. Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Dodecagon
Hexagon
n-gon
Heptagon
Hendecagon

4. Hip Bone’s connected to the… Classifying Polygons
Polygons with 3 sides… Triangles
Polygons with 4 sides… Quadrilaterals
Polygons with 5 sides.. Pentagons
But wait we have more polygons
Polygons with 6 sides… Hexagons
Polygons with 7 sides… Heptagons
Polygons with 8 sides… Octagons
But still we have more polygons
Polygons with 9 sides… Nonagons
Polygons with 10 sides… Decagons
Polygons with 12 sides… Dodecagons
And now we have our polygons

5. Important Terms A VERTEX is the point of intersection of two sides F A
CONSECUTIVE VERTICES are two endpoints of any side. F A B C D E
A segment whose endpoints are two
nonconsecutive vertices is called a DIAGONAL.
Sides that share a vertex are called CONSECUTIVE SIDES.

6. Polygons are named by listing its vertices consecutively.F E D

7. More Important Terms EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent

8. Three more important terms
Interior Angles
Exterior Angles
SUPPLEMENTARY
the SUM of an interior angle and it’s corresponding exterior angle = 180o

9. Polygons can be CONCAVE or CONVEX

10. Classify each polygon as convex or concave.

11. It’s what’s inside that counts 
Finding and using the interior angle measures of polygons

12. What is the sum of the measures of the interior angles of a triangle?
180°
180°
180°
What is the sum of the measures of the interior angles of any quadrilateral?
360°

13. Sum of measures of interior angles
# of triangles
Sum of measures of interior angles
# of sides
1(180) = 180 3 1
2(180) = 360 4 2 3
3(180) = 540 5 6 4
4(180) = 720
n-2
(n-2) 180 n

14. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

15. If you know the sum of the angles of a regular polygon, how can you find the measure of one of the congruent angles?
Regular Polygon
Interior angle sum
Measure of one angle
Triangle
180o
Quadrilateral
360o
Pentagon
Hexagon
Heptagon
Octagon
Decagon
Dodecagon
n-gon

16. If a regular convex polygon has n sides, then the measure of one of the interior angles is

17. HOMEWORK pg