5.1 Polygon Sum Conjecture

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Presentation transcript:

5.1 Polygon Sum Conjecture

Angle Exploration Equilateral Triangle 60°

Angle Exploration Square 90°

Angle Exploration Regular Pentagon 108°

Angle Exploration Regular Hexagon 120°

Angle Exploration Regular Heptagon 129°

Angle Exploration Regular Octagon 135°

Angle Exploration Regular Nonagon 140°

Angle Exploration Regular Decagon 144°

Angle Exploration Regular Dodecagon 147°

Angle Exploration Sides Degrees 3 60° 4 90° 5 108° 6 120° 7 129° 8 135° 9 140° 10 144° 11 147° Summarize our results Is there a correlation between the number of sides and the degrees?

Angle Exploration What is the sum of the angles in each of the polygons

Angle Exploration Sides Total Degrees 3 180° 60° 4 360° 90° 5 540° 108° 6 720° 120° 7 900° 129° 8 1080° 135° 9 1260° 140° 10 1440° 144° 11 1620° 147° Angle Exploration Summarize our results Total Degrees in each polygon. Do you see a pattern?

Interior Angles in a Polygon The sum of the angles of the interior angles of a convex n-gon is (n-2)•180°

Interior Angles in a Polygon What are the angle measures if the polygon is regular (n-2)•180°/n

Sample Problems

X=96

X=85

X=97

X=117

Exercise 12