The document outlines properties of angles in polygons, stating that the sum of the interior angles of a convex quadrilateral is 360 degrees and for an n-sided polygon it is (n-2)180 degrees. It emphasizes that the sum of exterior angles for any convex polygon is always 360 degrees. Examples demonstrate how to calculate the measures of angles in various polygons.

1. Angles in a
polygon

2. Property 1
•The sum of the measures of the angles
of a convex quadrilateral is 360.

3. Example 1: Angles of a Quadrilateral
Find the measure of :
A. in the figure on the right.

4. Solution:
Find the measure of
A. in the figure on the right.
•

5. Property 2
Polygon Interior Angles Sum
•The sum of the measures of
the angles of a convex
polygon with n sides is
(n-2)180

6. Example 2: Polygon Interior Angle Sum
•Find the sum of the measures of the interior angle of
each polygon.
• A. B.

7. Solution:
A. The polygon has 4 sides, so the sum of the
measures of the interior angle is:

8. Solution:
B. The polygon has 3 sides, so the sum of the
measures of the interior angles is:

9. Corollary
• The measure of each angle of
a regular n-gon is

10. Example 3: Corollary
•A. B.

11. Solution:
90

12. Solution:
B.
60

13. Property 3
•The sum of the measures of the
exterior angles, one at each
vertex, of any convex polygon is
360.

14. Example: Exterior Angle Sum of Regular Polygon
Find the value of x.
• A.

15. Solutions:
• A. Set the sum of the measures of the exterior angles equal to 360.
Polygon Exterior Angle Sum
Combine like terms
Subtract 186 from each side
Divide each side by 3

16. Example: Exterior Angle Sum of Regular Polygon
Find the value of x.
• B.

17. Solutions:
Polygon Exterior Angle Sum
Combine like terms
Subtract 106 from each side
Divide each side by 2

18. Thank you!