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What is a Polygon?• A polygon is a closed figure that is the

union of line segments in a plane.

• A polygon has three or more sides.

• A polygon has the same number of angles as sides.

Concave or Convex * In a convex polygon, each interior angle measures less

than 180 degrees.

*Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees.

Page 4: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Regular or not Regular

• A polygon is regular if all the sides and angles are equal in measure

Page 5: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Types of PolygonsPolygon Graphic Sides Angles Diagonals

(from one vertex)

Triangles Degrees

Page 6: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Polygon Graphic Sides Angles Diagonals Triangles Degrees

Page 7: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Polygon Graphic Sides Angles Diagonals Triangles Degrees

Page 8: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Interior Angles• Sum of Interior Angles of a Polygon= 180(n - 2)

(where n = number of sides)

Example 1: Find the number of degrees in the sum of the interior angles of an 14 – sided polygon.

Example 2: Find the number of degrees in the sum of the interior angles of an 20 – sided polygon,

Page 9: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Interior Angles• To find missing angles in a polygon

– 1. Find the total number of degrees in polygon.

– 2. Set up an equation equal to the number of degrees.

– 3. Solve equation.

Page 10: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Example

87°

x°

99° 99°

105°

Page 11: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Interior Angles• Each interior angle of a regular polygon =

where n = the number of sides in the polygon

Example 1: Find the number of degrees in each interior angle of a regular dodecagon.

Example 2: Each interior angle of a regular polygon measures 135°. How many sides does the polygon have?

Page 12: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

• Find the value of x.

9x 9x

12x 12x

Page 13: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Exterior Angles• An exterior angle of a polygon is an angle that forms a

linear pair with one of the angles of the polygon. For the hexagon shown at the left, <1

and <2 are exterior angles for that vertex.

Formula:Sum exterior angles of any polygon = 360°(using one exterior angle at a vertex)

Formula: Each exterior angle (regular polygon) =

Page 14: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

Exterior Angles• Example 1: Find the sum of the exterior angles of:

1. pentagon

2. decagon

3. a 15 sided polygon

4. a 7 sided polygon

* Example 2: Find the measure of each exterior angle of a regular hexagon.

Page 15: What is a Polygon? A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly1.htm

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly2.htm

http://www.regentsprep.org/Regents/math/geometry/GG3/PPoly3.htm

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