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Polygons

Polygons. Polygon Interior Angle Theorem. The sum of the measures of the interior angles of a convex polygon is given by: Sum = 180(n – 2) where n represents the number of sides in the polygon. Polygon Interior Angle Theorem. Find the sum of the measures of the interior angles of an octagon.

Polygons

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Presentation Transcript

1. Polygons

2. Polygon Interior Angle Theorem The sum of the measures of the interior angles of a convex polygon is given by: Sum = 180(n – 2) where n represents the number of sides in the polygon

3. Polygon Interior Angle Theorem • Find the sum of the measures of the interior angles of an octagon

4. Interior Angle of a Polygon • The find a single interior angle: Measure of Interior Angle = Interior Angle Sum n number of sides

5. Interior Angle of a Polygon • If a regular polygon has 14 sides, what is the measure of one of the interior angles?

6. Exterior Angles of a Polygon Polygon Exterior Angle Theorem The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°.

7. Exterior Angles of a Polygon • What is the sum of the measures of the exterior angles of a heptagon? • What is the sum of the measures of the exterior angles of a polygon with 324 sides?

8. Exterior Angle of a Polygon To find a single exterior angle: Exterior angle sum n number of sides

9. Exterior Angle of a Polygon • Find the measure of an exterior angle of a regular nonagon.

10. If an interior angle of a regular polygon measures 108°, how many sides does the polygon have?

11. Practice Problems

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