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