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Angles of a Polygon

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Angles of a Polygon Interior Angle Sum Theorem The sum of the measures of the interior angles of a convex polygon with n sides is (n - 2) 180. – PowerPoint PPT presentation

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Title: Angles of a Polygon


1
Angles of a Polygon
  • Diagonal of a polygon A segment that connects
    any two nonconsecutive vertices.
  • The number of triangles formed by drawing
    diagonals from one vertex of a polygon is always
    two less than the number of sides of the polygon,
    expressed as n-2.

2
Angles of a Polygon
  • Interior Angle Sum Theorem
  • The sum of the measures of the interior angles of
    a convex polygon with n sides is (n - 2)?180.
  • Since the angles in a regular polygon are
    congruent, you can find the measure of one
    interior angle of a regular polygon by dividing
    (n - 2)?180 by the number of angles, n. The
    formula for this is
  • (n - 2)?180
  • n

3
Example 1-1c
A decorative window is designed to have the shape
of a regular octagon. Find the sum of the
measures of the interior angles of the octagon.
Answer 1080
4
Example 1-2b
The measure of an interior angle of a regular
polygon is 144. Find the number of sides in the
polygon.
Answer The polygon has 10 sides.
5
Example 1-3d
Find the measure of each interior angle.
6
Angles of a Polygon
  • Exterior Angle Sum Theorem
  • The sum of the measures of the exterior angles of
    any convex polygon, one angle at each vertex, is
    360.
  • To find the measure of one exterior angle of a
    regular polygon, divide 360 by the number of
    sides.

7
Example 1-4c
Find the measures of an exterior angle and an
interior angle of convex regular hexagon ABCDEF.
Answer 60 120
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