8.1 Angles of polygons - Chino Valley Unified School District

8.1 ANGLES OF POLYGONS

Find and use the sum of the measures of the interior and exterior angles of a polygon

Polygon Interior Angles Sum

A DIAGONAL of a polygon is a segment that connects any two nonconsecutive vertices

Triangle Quadrilateral

Pentagon

Hexagon

180? 2 180? = 360? 3 180? = 540? 4 180? = 720?

Recall

A POLYGON is a closed figure formed by a finite number of coplanar segments called sides such that: the sides have a common endpoint that are not collinear and each side intersects exactly two other sides, but only at their vertices

Polygons

Sides 3 4 5 6 7 8 9 10 11 12 N

Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon

Decagon Hendecagon Dodecagon -

Measure of Interior Angles 1 180? = 180? 2 180? = 360? 3 180? = 540? 4 180? = 720?

5 180? = 900? 6 180? = 1080? 7 180? = 1260? 8 180? = 1440? 9 180? = 1620? 10 180? = 1800?

- 2 180?

Polygon Interior Angle Theorem

The sum of the interior angle measures of an -sided convex polygon - 2 180.

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