Objectives(2): Students will be able to find the sum of measures of the interior angles of a polygon. Students will be able to find the sum of the measures.

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Presentation transcript:

Objectives(2): Students will be able to find the sum of measures of the interior angles of a polygon. Students will be able to find the sum of the measures of the exterior angles of a polygon. Essential Questions: Explain the formula (n-2)180. Why is the sum of the exterior angles of any polygon always 360 degrees?

Polygons

Triangle – 3 sides Quadrilateral – 4 sides Pentagon – 5 sides Hexagon – 6 sides (think hex-six) Heptagon – 7 sides Octagon – 8 sides Nonagon – 9 sides (think non-nine) Decagon – 10 sides (think decimal-ten) Dodecagon – 12 sides

Interior Angles An interior angle is an angle inside the polygon.

Exterior Angles An exterior angle is the angle between any side of a shape and a line extended from the next side

Polygon Angle-Sum Theorem The sum of the measures of the interior angles of an n-gon is (n-2)180. Example 1

Example 2 The sum of the angle measures of a polygon with n sides is Find n. (n-2)180 = 1080 divide by 180 n-2 = 6 add 2 n = 8

To find the measure of each interior angle of a regular polygon, divide the total by the number of angles/sides. Example 3 What is the measure of each angle of a hexagon?

Polygon Exterior Angle-Sum Theorem The sum of the exterior angles of any polygon, regardless of the number of sides is always 360 degrees.

Every circle has a measure of 360 degrees. Since a regular polygon can be circumscribed by a circle, the measure of the exterior angles is 360 degrees

Finding a missing angle of a polygon. Example 4

To find the measure of one exterior angle of a regular polygon, divide 360 by the number of angles/sides.