Download exterior angle sum

Lesson 5.2
Polygon Exterior Angle Sum
HOMEWORK: 5.2/ 1-10
Polygon Exterior Angle Sum Theorem
The sum of the measures of the exterior angles
of any polygon, one at each vertex is 360.
m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360
2
Exterior angle sum = 360°
If and Only if
Example:
How many sides does a polygon have if it
has an exterior  measure of 36°.
= 36
360 = 36n
10 = n
Example:
Find the sum of the interior s of a polygon
if it has one exterior  measure of 24.
S = (n - 2)180
360 = 24
n
= (15 – 2)180
n = 15
= (13)180
= 2340
Example
Find x.
Using exterior angle sum:
Sum of the known exterior angles = 305 °
Exterior angle sum – 305 °
x = 360° – 305° = 55°
Example
How many sides does each regular polygon have
if its exterior angle is:
a. 120
b. 24
Ext sum
One angle
360
=3
120
360
= 15
24
3 sides
triangle
15 sides
Exterior Angles ONLINE!
• http://www.mathopenref.com/polygonexterio
rangles.html
• https://www.khanacademy.org/math/geomet
ry/parallel-and-perpendicularlines/triang_prop_tut/v/sum-of-the-exteriorangles-of-convex-polygon