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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.
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
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
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.
Find the measure of each interior angle.
Answer:
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.
Find the measures of an exterior angle and an interior
angle of convex regular hexagon ABCDEF.
Answer: 60; 120