6-1 The Polygon Angle-Sum Theorems

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6-1 The Polygon Angle-Sum Theorems

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Naming PolygonsPolygons are named by the number of sides they have.

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Finding a Polygon Angle SumPolygon Angle-Sum Theorem: The sum of the measures of the interior angles of an n-gon is (n – 2)180. What is the sum of the interior angle measures of a heptagon?

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 What is the sum of the interior angle measures of a 17-gon?

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Finding the Number of Sides of a PolygonThe sum of the interior angle measures of a polygon is 1980. How many sides does this polygon have? The sum of the interior angle measures of a polygon is 1440. How many sides does this polygon have?

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Using the Polygon Angle-Sum TheoremWhat is mY in pentagon TODAY?

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 What is mG?

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Regular PolygonsAn equilateral polygon is a polygon with all sides congruent. An equiangular polygon is a polygon with all angles congruent. A regular polygon is a polygon that is BOTH equilateral and equiangular.

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Corollary to the Angle-Sum TheoremThe measure of each interior angle of a regular n-gon is What is the measure of each interior angle in a regular hexagon?

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 What is the measure of each interior angle in a regular nonagon?

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Exterior AnglesYou can draw exterior angles at any vertex of a polygon. Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon (one at each vertex) is 360.

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Finding an Exterior Angle MeasureWhat is m1 in this regular octagon?

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 What is the measure of an exterior angle of a regular nonagon?

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Last Updated: 8th March 2018

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