1. The Polygon Angle-Sum Theorem

2. NUMBER OF SIDES
NAME 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon

3. The Polygon Angle-Sum Theorem
A diagonal is a segment that connects two nonconsecutive vertices in a polygon!

4. The Polygon Angle-Sum Theorem
Essential Understanding:
The sum of the interior angle measures of a polygon depends on the number of sides the polygon has.
By dividing a polygon with n sides into (n – 2) triangles, you can show that the sum of the interior angle measures of any polygon is a multiple of 180.

5. The Polygon Angle-Sum Theorem
Problem 1: Finding a Polygon Angle Sum
What is the sum of the interior angle measures of a heptagon?

6. The Polygon Angle-Sum Theorem
Problem 1b: Finding a Polygon Angle Sum
What is the sum of the interior angle
measures of a 17-gon?

7. The Polygon Angle-Sum Theorem
Problem 1c:
The sum of the interior angle measures of a polygon is How can you find the number of sides in the polygon? Classify it!

8. The Polygon Angle-Sum Theorem
Problem 1d:
The sum of the interior angle measures of a polygon is How can you find the number of sides in the polygon? Classify it!!!

9. The Polygon Angle-Sum Theorem

10. The Polygon Angle-Sum Theorem

11. The Polygon Angle-Sum Theorem
Problem 2:
What is the measure of each interior angle in a regular hexagon?

12. The Polygon Angle-Sum Theorem
Problem 2b:
What is the measure of each interior angle in a regular nonagon?

13. The Polygon Angle-Sum Theorem
Problem 2c:
What is the measure of each interior angle in a regular 100-gon?
Explain what happens to the interior angles of a regular figure the more sides the figure has? What is the value approaching but will never get to?

14. The Polygon Angle-Sum Theorem
Problem 3:
What is m<Y in pentagon TODAY?

15. The Polygon Angle-Sum Theorem
Problem 3b:
What is m<G in quadrilateral EFGH?

16. The Polygon Angle-Sum Theorem
You can draw exterior angles at any vertex of a polygon. The figures below show that the sum of the measures of exterior angles, one at each vertex, is 360.

17. Problem 4: What is m<1 in the regular octagon below?

18. What is the measure of an exterior angle of a regular pentagon?
Problem 4b:
What is the measure of an exterior angle of a regular pentagon?

19. Problem 5:
What do you notice about the sum of the interior angle and exterior angle of a regular figure?

20. Problem 6:
If the measure of an exterior angle of a regular polygon is 18. Find the measure of the interior angle. Then find the number of sides the polygon has.

21. Problem 6b:
If the measure of an exterior angle of a regular polygon is 72. Find the measure of the interior angle. Then find the number of sides the polygon has.

22. Problem 6c:
If the measure of an exterior angle of a regular polygon is x. Find the measure of the interior angle. Then find the number of sides the polygon has.