3.5 Polygon Angle Sum Theorem - Poudre School District

3.5 Polygon Angle Sum Theorem

October 09, 2009

35 Polygon Angle Sum Theorem

Objectives

Explore the patterns found in the angles of polygons. Identify formulas for finding interior and exterior angles of a polygon.

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3.5 Polygon Angle Sum Theorem

October 09, 2009

EXPLORATION

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3.5 Polygon Angle Sum Theorem

October 09, 2009

Number of sides (n) Number of triangles formed

4 5 6 7 8

Sum of interior angles

Sum of exterior angles

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3.5 Polygon Angle Sum Theorem

October 09, 2009

4 sides

5 sides

6 sides

___ triangles

___ triangles

___ triangles

7 sides = ___ triangles 8 sides = ___ triangles

n sides = _____ triangles

A triangle has 180 degrees, so multiply the number of

triangles by 180.

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3.5 Polygon Angle Sum Theorem

October 09, 2009

Number of sides (n) Number of triangles (n2)

4

(42) = 2

5

(52) = 3

6

(62) = 4

7

(72) = 5

8

(82) = 6

Sum of interior angles (n2)180

(42)180 = 360

(52)180 = 540 (62)180 = 720 (72)180 = 900

(82)180 = 1080

Sum of exterior angles

n

(n2) =

(n2)180 =

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