section 3-5 angles of a polygon. polygon means: “many-angled” a polygon is a closed figure...
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Section 3-5Angles of a
Polygon
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Polygon
• Means: “many-angled”
• A polygon is a closed figure formed by a finite number of coplanar segments
a. Each side intersects exactly two other sides, one at each endpoint.
b. No two segments with a common endpoint are collinear
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Ex #1
Examples of polygons:
Ex#2
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Two Types of Polygons:
1. Convex: If a line was extended from the sides of a polygon, it will NOT go through the interior of the polygon.
Ex #1
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2. Nonconvex: If a line was extended from the sides of a polygon, it WILL go through the interior of the polygon.
Ex#2
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Polygons are classified according to the number of sides they have.
*Must have at least 3 sides to form a polygon.
Special names
for Polygons
Number of Sides
Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
n n-gon*n stands for number of sides.
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Diagonal
• A segment joining two nonconsecutive vertices
*The diagonals are indicated with dashed lines.
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Definition of Regular Polygon:
• a convex polygon with all sides congruent and all angles congruent.
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Interior Angle Sum Theorem
• The sum of the measures of the interior angles of a convex polygon with n sides is
S = 180 (n - 2)
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One can find the measure of each interior angle of a regular polygon:
1. Find the Sum of the interior angles
2.Divide the sum by the number of sides the regular polygon has.
S = 180 (n - 2)
n
S
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One can find the number of sides a polygon has if given the measure of an interior angle
n
n 2180
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Exterior Angle Sum Theorem
• The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.
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One can find the measure of each exterior angle of a regular polygon:
360
n = exterior angle
or
360
exterior angle = n
One can find the number of sides a polygon has if given the measure of an exterior angle