1. 5.1 Polygon Sum Conjecture pg. 256 to 259
Warm Up: pg. 259 # 18, pg. 263 # 15, 16 R D
18. x=120°
15. Yes, ΔRAC≅ΔDCA by SAS A
AD≅CR by CPCTC C
16. Yes. ΔDAT≅ΔRAT by SSS D
<D≅<R by CPCTC
A
T
R

2. Pg. 256
Investigation--
No. of polygon sides 3 4 5 6 7 8 .... n
Sum of angle meas. 180° 360° 540° 720° 900° 1080° .... 180°(n-2)
What does this mean???
--You can either MEMORIZE all the degrees for EVERY
SHAPE EVER or you can use the formula
180°(n-2) (used to find the SUM of the
ANGLES of ANY POLYGON)
180° --sum of angles in triangle
(n-2) represents # of Δ's in the polygon when divided by diagonals
from ONE vertex

3. 5.2 Exterior Angles of Polygons
Sum of Exterior Angles
Answer is ALWAYS 360°
That is the ONLY answer, EVER!!!!!
Why??
if you take ALL of the verticies of ANY polygon and pull
them into the center of that polygon--it forms a CIRCLE
EACH Interior Angle measure
ONLY works with regular polygon because all the
angles are equal!!!
Uses the Polygon Sum formula and then divides by
the number of angles--same as the number of
sides!!!!
180° (n-2)
n

4. TO Summarize Sections 5.1 and 5.2...:
Formula for:
180° (n - 2)
Each interior angle: n
Sum of exterior Angles: 360°
Each exterior angle: 360°
n
Sum of Interior angles: 180° (n - 2)

5. The trick is to READ and EXAMINE the
diagram...
**Know what they are looking for....
EX.

6. EXAMINE the diagram...
1st... How many sides? 7
(so that means n=7)
2nd...Use the SUM of interior angles formula
180°(n-2)
Substitute 7 for n and do the math...
Sum for a heptagon is 900°
3rd... Subtract all the angles from 900° to
get answer...145°

7. What if they want EACH interior angle of a
polygon?
READ and EXAMNIE picture....
What is the measure of an interior angle in a
regular pentagon?
*What is n? =--- 5
*What formula=---- 180°( n - 2)/ n
Substitute 5 for n...
180°( 5 -2) / 5
= 108° Why this one?
BECASUE they want "an" angle
not the SUM
THIS ONLY WORKS ON REGULAR POLYGONS!!!!

8. Sometimes they give you this....
Find each interior angle measure of this
regular polygon
Ask yourself.. What is it?
Pentagon (5 sides so n = 5)
USE formula for EACH interior angle: 180°(n-2)/n
substitute and solve!

9. Exterior Angle Sum:
How does that work????
Think!--If the shape sucks itself into the center, what
are you left with?
Right!--A circle which is 360°
DOESN"T matter which polygon--ALL polygons
have EXTERIOR ANGLE SUMS of 360°

10. Try it...
1. What is the sum of the measures of the exterior
angles of a pentagon? 360°
2. The sum of the measures of the exterior angles
of a 30-gon is___360°__
3.
b
a
d
c
what is the sum of the
lettered angles? 360°

11. Lastly if the SUM of the
exterior angles of a polygon is
360°....
How do you get EACH exterior angle of
a polygon?
1. It HAS to be a regular polygon! Other
wise this will not work!
2. Take the sum 360° and divde by the
number of sides! 360°/n

12. Example.....
What is the measure of each exterior angle of
a regular hexagon?
1. Identify n! (6)
2. Plug in 360°/ 6
3. Solve.. 60°
the words tell you what
formula to use

13. Try these videos......
Polygon sum formula
http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch03/03-04/PH_Geom_ch03-
04_Obj2_vid1.html
Exterior Angle Sum
Try the Dynamic exploration on Textbook link!