1. PIB Geometry
3-5: Polygons

2. Homework 3-4 Questions?

3. 3-5 Objectives
Recognize and name convex polygons and regular polygons.
Investigate and apply the Polygon Interior Angle Sum Theorem.
Investigate and apply the Polygon Exterior Angle Sum Theorem.

4. Angles of a Polygon Investigation
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5. Theorem 3-13: Polygon Interior Angle Sum Theorem The sum of the measures of the interior angles of a convex polygon with 𝑛 sides is: Theorem 3-14: Polygon Exterior Angle Sum Theorem The sum of the measures of the exterior angles of a convex polygon with 𝑛 sides is:

6. In case you missed it:

7. Examples
Find the sum of the measures of the interior angles of a heptagon.
Find the sum of the measures of the exterior angles of a heptagon.

8. Def: A polygon is regular if it is both equilateral and equiangular.
What is the measure of each interior angle of regular n-gon?
Each exterior angle?

9. Examples. Solve for 𝑚∠𝐴

10. Example
The measure of one interior angle of a regular polygon is the sum of the measures of its exterior angles. How many sides does the polygon have?

11. Example
The sum of the measures of the interior angles of a regular polygon is 24 times the measure of one exterior angle. How many sides does the polygon have?

12. Polygons