Angles of a Polygon

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Section 3-5

• Angles 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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Examples of polygons
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Two Types of Polygons

• Convex If a line was extended from the sides of
  a polygon, it will NOT go through the interior of
  the polygon.

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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.

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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

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

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One can find the measure of each interior angle
of a regular polygon

• Find the Sum of the interior angles
• Divide the sum by the number of sides the regular
  polygon has.

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One can find the number of sides a polygon has if
given the measure of an interior angle
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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
One can find the number of sides a polygon has if
given the measure of an exterior angle