Do Now

Take out your calculator.

Take a protractor from the front.

In your notebook answer the following questions:

1. How many sides does a pentagon have?

2. Draw a hexagon.

3. What shape has 7 sides?

Compton Jr. Posse

Polygon Sum Conjecture

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

Polygons

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

11—gon

Dodecagon

13—gon

N-gon

Investigation

1. Draw the polygon. Carefully measure all the interior angles, then find the sum.

2. 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.

3. 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

Quadrilateral sum Conjecture

The sum of the measures of the four interior angles of any quadrilateral is _____.

360o .

Pentagon sum Conjecture

The sum of the measures of the five interior angles of any pentagon is _____.

540o .

Polygon Sum Conjecture

How many sides?

How many triangles?

How many degrees?

Polygon sum Conjecture

The sum of the measures of the n interior angles of any n—gon is _____.

180o(n—2) .

Regular Polygons

Regular Polygons—Equilateral and equiangular

Equilateral—all n sides are congruent.

Equiangular—all n interior angles are congruent.

Regular polygons.

Find the measure of each interior angle.

Polygon sum Conjecture

In a regular polygon, the measure of each interior angle of any n—gon is _____.

180o(n—2) . n

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Practice

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

Exit Slip

In each problem, show your work AND explain your reasoning.

1. How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents.

2. What is the measure of each angle of a regular octagon?

3. Find the measure of x.

Honors Exit Slip In each problem, show your work AND explain your reasoning.

1. How many degrees are in a 45-gon? Include in your explanation what each part of the formula represents.

2. What is the measure of each angle of a regular octagon?

3. Find the measure of w, x, y, and z.