Chapter 2.notebook
February 15, 2017
Section 2.4 - Angle Properties in Polygons
Explore:
A pentagon has 3 right angles and 4 sides of equal lengths, as shown. What is the sum of the angles in the pentagon?
Convex Polygon ­ a polygon in which each interior angle measures less than 1800.
Convex
non­convex (concave)
The sum of the measures of the interior angles of a convex polygon can be expressed as:
S(n) = 180(n ­ 2)
Polygon Number of Sides
triangle 3
quadrilateral
4
pentagon
5
hexagon
6 Heptagon
7 octagon
8 Number of Triangles
Sum of Angle Measures
Names of Different Polygons
Number of Sides
3
4
5
6
7
8
9
10
11
12
Name of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
where: n is the number of sides of the polygon
S(n) is the sum
Regular Polygons: Polygons in which each side is of equal length
Example:
Example 1
Outdoor furniture and structures like gazebos sometimes use a regular hexagon in their building plan. a) What is the sum of the interior angles in the hexagon? For regular polygons, the following formula can be used to determine the measure of each individual angle:
b) Determine the measure of each interior angle of a regular hexagon.
The sum of the measures of the exterior angles of any convex polygon is 3600.
Chapter 2.notebook
TRY
Determine the sum of the interior angles and the measure of each interior angle of a regular 15­sided polygon (pentadecagon).
TRY
The sum of the measures of the interior angles of an unknown polygon is 12600. What type of polygon is it?
TRY
Determine the measure of each exterior angle of a 13 sided polygon.
February 15, 2017
Example 2 The sum of the measures of the interior angles of an unknown polygon is 9000. What type of polygon is it?
Example 3
Determine the measure of each exterior angle of a dodecagon.
Practice Problems
Pgs 99 - 102
#'s 1-3, 6, 8, 10, 11, 17