Angles of a Polygon Diagonal of a polygon – A segment that connects any two nonconsecutive vertices. The number of triangles formed by drawing diagonals.

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Presentation transcript:

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 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 Example 1-1c

Answer: The polygon has 10 sides. 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. Example 1-2b

Find the measure of each interior angle. Answer: Example 1-3d

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 Example 1-4c