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Polygon Angle-Sum Theorem
Polygon Angle-Sum Theorem
G.CO.9 Prove theorems about lines and angles...
Goals for this section:
Goals for this section:
Students should be able to figure out a missing angle in a polygon and to know how to find exterior angles.
Polygon Angle-Sum Theorem
Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is:
The sum of the measures of the interior angles of an n-gon is:
(n-2)*180
(n-2)*180
n is the number of sides in the polygon
n is the number of sides in the polygon
Example:
Example:
Find the measure of each angle.
Find the measure of each angle.
Answer:
Equilateral Polygon
Equilateral Polygon
All sides have the same length.
All sides have the same length.
Equiangular Polygon
Equiangular Polygon
All angles have the same measure.
All angles have the same measure.
Regular Polygon
Regular Polygon
All sides have the same length AND all angles have the same measure.
All sides have the same length AND all angles have the same measure.
The measure of an angle in a regular polygon
The measure of an angle in a regular polygon
The measure of each interior angle of a regular n-gon is
The measure of each interior angle of a regular n-gon is
Example:
Example:
What is the measure of the angles in a regular triangle?
What is the measure of the angles in a regular triangle?
Answer:
Polygon Exterior Angle-Sum Theorem
Polygon Exterior Angle-Sum Theorem
The sum of all the exterior angles of a polygon is equal to 360.
The sum of all the exterior angles of a polygon is equal to 360.
Keywords: interior angles, exterior angles, equilateral, equiangular, regular, polygon
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