Warm Up: pg. 259 # 18, pg. 263 # 15, 16

18. x=120°

15. Yes, ΔRAC≅ΔDCA by SASAD≅CR by CPCTC

16. Yes. ΔDAT≅ΔRAT by SSS<D≅<R by CPCTC

R

A

D

C

D

A

R

T

5.1 Polygon Sum Conjecture pg. 256 to 259

Pg. 256Investigation--

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 diagonalsfrom ONE vertex

No. of polygon sides 3 4 5 6 7 8 .... n Sum of angle meas. 180° 360° 540° 720° 900° 1080° .... 180°(n-2)

5.2 Exterior Angles of Polygons

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 measureONLY 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

Sum of Exterior Angles

TO Summarize Sections 5.1 and 5.2...:

Formula for:

Each interior angle:

Sum of exterior Angles:

Each exterior angle:

Sum of Interior angles:

360°

360°n

n

180° (n - 2)

180° (n - 2)

The trick is to READ and EXAMINE the diagram...

**Know what they are looking for....

EX.

EXAMINE the diagram...

1st... How many sides? 7 (so that means n=7)

2nd...Use the SUM of interior angles formula180°(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°

Why this one? BECASUE they want "an" angle not the SUM

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°

THIS ONLY WORKS ON REGULAR POLYGONS!!!!

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!

Think!--If the shape sucks itself into the center, what are you left with?

Right!--A circle which is 360°

Exterior Angle Sum:How does that work????

DOESN"T matter which polygon--ALL polygons have EXTERIOR ANGLE SUMS of 360°

what is the sum of the lettered angles? 360°

ab

cd

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.

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

Example.....

What is the measure of each exterior angle of a regular hexagon?

1. Identify n! (6)2. Plug in 360°/ 63. Solve.. 60°

the words tell you what formula to use

http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-037878-X/Ch03/03-04/PH_Geom_ch03-04_Obj2_vid1.html

Try these videos......Polygon sum formula

Exterior Angle Sum

Try the Dynamic exploration on Textbook link!