Bell Work

1. Find x 2. Find x and y

PolygonsDay 1 – Interior Angles

This is a chartPolygon # of Sides # of Triangles Sum of the

Angle Measures

Interior Angle Measures

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

N-gon

3

4

5

6

7

8

n

1

2

3

4

5

6

n -2

Example 1

• Ryan’s parents are building him a sandbox to play in. It is the shape of a hexagon as shown. What is the sum of the measures of the interior angles of the hexagon?

Example 2• The sum of the angles inside a polygon is 2340 degrees. Find

the number of sides on this polygon.

Example 3

• Find the value of x.

Example 4

• Find the value of x.

Regular (Defn)• Definition:

• Can you name a regular quadrilateral?• A regular triangle?

How do we find interior angles?Polygon # of Sides # of Triangles Sum of the

Angle Measures

Interior Angle Measures

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

N-gon

3

4

5

6

7

8

n

1

2

3

4

5

6

n-2

180

360

540

720

900

1080

180(n-2)

Example 5• A regular polygon with each interior angle is 140 degrees. How

many sides does the polygon have?

HOMEWORK• 6.1 Pg 320 #’s 1-3, 7-9, 13-15, 19-20

Bell Work• A mall is designed so that 5

walkways meet at a food court that is in the shape of a regular pentagon. Find the sum of the measures of the interior angles of the pentagon.

• A polygon that has 53 sides has how many degrees in all of their interior angles?

PolygonsDay 2 – Exterior Angles

Sum of Exterior Angles• An exterior angle is formed when one side at a vertex of a

polygon is extended.• The sum of ALL the exterior angles is 360. FOR EVERY

POLYGON!!!• This is because the angles rotate around to make one

revolution. (circle-has 360 degrees)

Example 1• Find the sum of the exterior angles and the measure of each

exterior angle of a…1. quadrilateral

2. 100-gon

3. nonagon

Example 2• A hexagon has an exterior angle that measures…

• The formula for each exterior angle is:

Example 3• A polygon has an exterior angle of 18 degrees. How many

sides does the polygon have?

Example 4• Find the interior and exterior angle measure of a dodecagon

Challenge• The ratio for an exterior angle to an interior angle is 1:3. How

many sides are in the shape.

Homework• 6.1 Pg 321 #’s 10, 16, 17, 23-26, 31