1. 5.2 Exterior Angles of a Polygon
HOMEWORK: Lesson 5.2/1-10

2. Polygon Exterior  Sum Theorem
The sum of the measures of the exterior s of a polygon
is 360°.
Only one exterior  per vertex. 1 2 3
m1 + m2 + m3 + m4 + m5 = 360 5 4
The interior  & the exterior  are Supplementary.
Int + Ext = 180

3. Polygon Exterior Angle-Sum Theorem
The sum of the measures of the angles of a polygon, one at each vertex, is
ex: This pentagon
has 5 sides.
The sum of the 5
exterior angles is
360.
Exterior
360.

4. ONE Exterior Angle
For Regular Polygons
measure of One Exterior  =

5. Example 360 120 360 24 = 3 = 15 3 sides 15 sides 𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒
How many sides does each regular polygon have if its exterior angle is: a. 120 b. 24
360
120
𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒
= 3
= 15
3 sides
15 sides

6. Exterior Angle Sum
What is the measure of an interior angle of a regular octagon? (use the exterior angle)
Solution:
one ext  =
exterior angle = 45°
interior angle = 180 – exterior angle
interior angle = 180 – 45 = 135°

7. 𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒 = 360° 36° = 10 sides
Example:
How many sides does a polygon have if it has an exterior  measure of 36°.
𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒 = 360° 36° = 10 sides
𝑛=10 𝑠𝑖𝑑𝑒𝑠

8. Example: S = (n - 2)180 = (15 – 2)180 = (13)180 S = 2340°
Find the sum of the interior s of a polygon if it has one exterior  measure of 24°.
𝑛= 𝑒𝑥𝑡 𝑠𝑢𝑚 𝑜𝑛𝑒
𝑛= = 15 sides
S = (n - 2)180
= (15 – 2)180
= (13)180
S = 2340°

9. Example 360˚ = x + 305 ˚ x = 360˚ – 305 ˚ = 55˚ Find x.
=305

10. Example
How many sides does each regular polygon have if its exterior angle is:
a. 120 b. 24
𝑛= 360 𝐸𝑎𝑐ℎ
𝑛= 360 𝐸𝑎𝑐ℎ
𝑛= 360° 120°
𝑛= 360° 24°
𝑛=3 sides
𝑛=15 sides

11. Example
How many sides does each regular polygon have if its interior angle is:
a. 90 b. 144
𝐸𝑎𝑐ℎ= 𝑛−2 180° 𝑛
𝐸𝑎𝑐ℎ= 𝑛−2 180° 𝑛
144°= 𝑛−2 180° 𝑛
90°= 𝑛−2 180° 𝑛
90°𝑛= 𝑛−2 180°
144°𝑛= 𝑛−2 180°
90°𝑛=180°𝑛−360
144°𝑛=180°𝑛−360
−36°𝑛=−360
−90°𝑛=−360
𝑛= 4 sides
𝑛= 10 sides

12. Summary: SUM of the Interior Angles of a Polygon S = (n – 2) 180
One Interior Angle of a REGULAR Polygon
One  = (n – 2) 180 n
SUM of the Exterior Angles of a Polygon
SE = 360
One Exterior Angle of a REGULAR Polygon
OneEx  = 360 n