1. Do Now Take out your calculator. Take a protractor from the front.
In your notebook answer the following questions:
How many sides does a pentagon have?
Draw a hexagon.
What shape has 7 sides?

2. Compton Jr. Posse

3. Polygon Sum Conjecture

4. Today’s Objectives Discover the sum of the angle measures in a polygon
Write formulas for the measure of the interior angle of an equiangular polygon.
Use problem solving skills

5. Polygons Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon
Nonagon
Decagon
11—gon
Dodecagon
13—gon
N-gon

6. Investigation
Draw the polygon. Carefully measure all the interior angles, then find the sum.
Share your results with your group. If you measured carefully, you should all have the same sum! If your answers aren’t exactly the same, find the average.
Copy the table. Repeat steps 1 and 2 for different polygons.
# of sides of polygon 3 4 5 6 7 8 … n
Sum of measures of angles

7. Quadrilateral sum Conjecture
The sum of the measures of the four interior angles of any quadrilateral is _____.
360o .

8. Pentagon sum Conjecture
The sum of the measures of the five interior angles of any pentagon is _____.
540o .

9. Polygon Sum Conjecture
How many sides?
How many triangles?
How many degrees?

10. Polygon sum Conjecture
The sum of the measures of the n interior angles of any n—gon is _____.
180o(n—2) .

11. Regular Polygons Regular Polygons—Equilateral and equiangular
Equilateral—all n sides are congruent.
Equiangular—all n interior angles are congruent.

12. Regular polygons.
Find the measure of each interior angle.

13. Polygon sum Conjecture
In a regular polygon, the measure of each interior angle of any n—gon is _____.
180o(n—2) . n

14. Practice

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25. Practice

26. Today’s Objectives Discover the sum of the angle measures in a polygon
Write formulas for the measure of the interior angle of an equiangular polygon.
Use problem solving skills

27. Exit Slip In each problem, show your work AND explain your reasoning.
How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents.
What is the measure of each angle of a regular octagon?
Find the measure of x.

28. Honors Exit Slip
In each problem, show your work AND explain your reasoning.
How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents.
What is the measure of each angle of a regular octagon?
Find the measure of w, x, y, and z.