8.2 Angles in Polygons

1
8.2 Angles in Polygons

• Textbook pg 417

2
Interior and Exterior Angles
exterior angle
exterior angle
exterior angle
interior angles
exterior angle
exterior angle
3
Polygon Exterior Angles Theorem

• The sum of the exterior angles of a convex
  polygon is always 3600

4
Polygon of sides of Triangles Sum of Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
5
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
6
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
7
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
8
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
9
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon
Nonagon
Decagon
Dodecagon
n-gon
10
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon 8 6 10800
Nonagon
Decagon
Dodecagon
n-gon
11
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon 8 6 10800
Nonagon 9 7 12600
Decagon
Dodecagon
n-gon
12
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon 8 6 10800
Nonagon 9 7 12600
Decagon 10 8 14400
Dodecagon
n-gon
13
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon 8 6 10800
Nonagon 9 7 12600
Decagon 10 8 14400
Dodecagon 12 10 18000
n-gon
14
Polygon of sides of Triangles Sum of Interior Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon 5 3 5400
Hexagon 6 4 7200
Heptagon 7 5 9000
Octagon 8 6 10800
Nonagon 9 7 12600
Decagon 10 8 14400
Dodecagon 12 10 18000
n-gon n n 2 (n 2) 1800
15
Polygon Interior Angles Theorem

• For any convex polygon with n sides, the sum of
  the interior angles can be found with the
  following formula
• (n 2) 1800