Download Angles and Polygons

Angles and Polygons
Course: Geometry
Topic: Angles and Polygons
Objective: Find the sum of interior angles of polygons. Find measure of exterior angles of
polygons.
Body:
Interior Angle Sum Theorem
If a convex polygon has n sides and S is the sum of the measure of its interior angles,
Then S = 180(n-2)
Example:
Find the sum of the measures of the interior angles of a polygon with 32 sides.
In a 32-gon n = 32
n being identified as number of sides
S = 180(32-2)
plug into formula
S = 180(30)
simplify
S = 5400
Example:
The measure of an interior angle of a regular polygon is 140 find the number of sides in the
polygon.
Use formula S = 180(n-2)
S = 140n
If one angle is 140, then sum is 140 times the number of sides.
140n = 180(n-2)
Plug into formula
140n = 180n-360
Simplify
360 = 40n
n=9
Exterior Angle Sum Theorem
If a polygon is convex, then the sum of the measure of the exterior angles, one at each vertex, is
360.
Example
Find the measure of an exterior angle and on interior angle of a convex regular octagon.
How many sides does an octagon have? 8
The sum of the measures of the interior angles
S = 180(n-2) use n=8
S = 180 (8-2) = 1080
Divide 1080 by 8 to get the measure of an interior angle
1080/8=135
To find the measure of an exterior angle, one exterior angle at each angle makes a total of 8
angle. All those angles should add up to 360, so.
8n = 360
n = 45