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