5.2 Polygon Exterior Angles

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Interior and Exterior Angles of Polygons

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Presentation transcript:

5.2 Polygon Exterior Angles

What is an interior angle? Any of the six angles inside the polygon

What is an exterior angle? When the sides of the polygon are extended, the angle that is adjacent to the interior angle

What is an exterior angle? When the sides of the polygon are extended, the angle that is adjacent to the interior angle

Spot the exterior angle

Exterior Angles Which side do you extend to create an exterior angle?

Exterior Angles Either one, these two angles are congruent, because they are vertical angles.

Exterior angle What is the value of all the exterior angles in any polygon?

Exterior Angle Investigation Get your supplies Printer Paper Straightedge Protractor

Exterior Angle Investigation Draw a large polygon on your paper Pentagon or larger Extend each of its sides to form exterior angles

Exterior Angle Investigation Measure all of the interior angles except one. Write the value of the interior angle on the angle. Use the polygon sum conjecture to calculate the measure of the last angle before you measure it.

Exterior Angle Investigation Use the linear pair conjecture to calculate the value of each exterior angle. Write down the value on the angle Add up all the exterior measures

Exterior Angle Theorem The sum of the measures of the exterior angles of a convex polygon, (one angle at each vertex), is 360°

Exterior angle What is the measure of an exterior angle in a regular polygon?

Exterior Angle Theorem The measure of each exterior angle of a regular n-gon is 360°/n

Equiangular Polygon Conjecture You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: 180° - 360°/n (180°(n-2))/n

Practice Problems

Homework Worksheet 5-1 Worksheet 5-2