6.1 Notes The Polygon Angle-Sum Theorem. Investigation Sketch a polygon with 4,5,6, and 8 sides. Divide each polygon into triangles by drawing all diagonals.

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The Polygon Angle-Sum Theorems

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Presentation transcript:

6.1 Notes The Polygon Angle-Sum Theorem

Investigation Sketch a polygon with 4,5,6, and 8 sides. Divide each polygon into triangles by drawing all diagonals possible from one vertex. Fill in the table based on the number of triangles. Polygon# of sides# triangles formed Sum of interior angle measures Quadrilateral4_______(180) =

Polygon Angle-Sum Theorem The sum of the measures of the angles of an n-gon is (n-2)180. Find the sum of the measure of the angles of a 15-gon. The sum of the measure of the angles of a polygon is 720. What type of polygon is it?

Regular Polygons What is the measure of one interior angle of a regular hexagon?

Using the Polygon Angle- Sum Theorem

Polygon Exterior Angle- Sum Theorem Let’s draw all the exterior angles on this pentagon. Make a conjecture about the sum of the exterior angles of this polygon? Of any n-gon? What is the measure of one exterior angle of a regular pentagon?

Lesson Check: What is the sum of the interior angle measures of an 11-gon? What is the sum of the measures of the exterior angles of a 15-gon? Find the measures of an interior and an exterior angle of a regular decagon? Interior angle = 144 Exterior angle = 36

6.1 HW On mathxlforschool.com due Sunday at midnight