12.4 REGULAR POLYGONS AND TESSELLATIONS

Central Angle of a Polygon

The measure of each central angle in a regular n-gon is n

360.

To Do: The measure of each central angle of a regular polygon is 24 . How many sides are there?

?

Vertex Angles

Vertex Angles

Total = 3 180 = 540

Each vertex angle measures 540/5 = 108

Measure of the Vertex Angles in a Regular n-gon

Each vertex angle will measure n

n 180)2(

Remember also that each central angle measures n

360

n n

n 180)2(

n360

3 60 120 4 90 90 5 108 72 6 120 60

Conclusion: Each vertex angle is the supplement of any central angle.

Measure of the Vertex Angles in a Regular n-gon

Conclusion: Each vertex angle is the supplement of any central angle.

Central Angle Vertex Angle

Each vertex angle will measure n

n 180)2(.

Also, each vertex angle is the supplement of any central angle.

To Do: What is the measure of each vertex angle of a regular 16-gon?

To Do: Each vertex angle of a regular polygon has measure 162 . How many sides are there?

To Do: Each vertex angle of a regular polygon has measure 176 . What is the measure of each central angle?

Tessellations with Regular Polygons

Let’s look at some Web sites

Let’s look at some activities

12.4 A 2 3 4 5 6 8 23 12.4 B 12a