Download A polygon is a simple closed figure formed by three or more line

Sec. 5-4 Polygons and Angles
Monday, January 30, 2017
12:15 PM
A polygon is a simple closed figure formed by three or
more line segments. The segments intersect only at their
endpoints.
Interior Angle Sum of a Polygon: The sum of the
measures of the interior angles of a polygon is (n - 2)180,
where n represents the number of sides.
S = (n - 2)180
You can use the sum of the angle measures of a triangle
to find the sum of the interior angle measures of various
polygons. A polygon that is equilateral (all sides are the
same length) and equiangular (all angles have the same
measure) is called a regular polygon.
Number of Sketch of Number of
Sides
Figure Triangles
3
1
4
2
5
3
6
4
Math - regular class Page 1
Sum of Angle
Measures
1(180)=180°
2(180)=360°
3(180)=540°
4(180)=720°
Ex. Find the sum of the measures of the interior angles
of a decagon.
Ex. Find the sum of the interior angle measures of each
polygon.
a) hexagon
b) octagon
c)
15-gon
Ex. Each chamber of a bee honeycomb is a regular
hexagon. Find the measure of an interior angle of a
regular hexagon.
Math - regular class Page 2
Exterior Angles of a Polygon: In a polygon, the sum of
the measures of the exterior angles, one at each vertex,
is 360°.
Regardless of the number of sides in a polygon, the sum
of the exterior angle measures is equal to 360°.
Ex. Find the measure of an exterior angle in a regular
hexagon.
Ex. Find the measure of an exterior angle of each regular
polygon.
a) Triangle
b) quadrilateral
c)
octagon
Math - regular class Page 3
Find the sum of the interior angle measures of each
polygon.
1. quadrilateral
2. nonagon
3. 12-gon
4. If you have an equilateral triangle, what is the
measure of one interior angle of an equilateral triangle?
5. Find the measure of an exterior angle of a regular
pentagon.
Homework: Sec. 5-4 p.401 #1-15
Math - regular class Page 4
Math - regular class Page 5