Scales Triangles/A ngles Cross Sections Circles Measurements 10 20 30 40.
6-1 A NGLES OF A P OLYGON. POLYGON: A MANY ANGLED SHAPE SidesName 3Triangle 4Quadrilateral 5Pentagon...
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Transcript of 6-1 A NGLES OF A P OLYGON. POLYGON: A MANY ANGLED SHAPE SidesName 3Triangle 4Quadrilateral 5Pentagon...
6-1 ANGLES OF A POLYGON
POLYGON: A MANY ANGLED SHAPE
Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
8 Octagon
10 Decagon
n n-gon
# sides = # angles = #vertices
SOME INFO:
Regular Polygon: all angles are equal Diagonal: a segment connecting 2
nonconsecutive vertices.
DIAGONALS (Look at these, don’t write in notes) Quadrilateral
Look! 2 triangles 2(180) = 360 Sum of the angles of a quadrilateral is 360
Pentagon 3 triangles 3(180) = 540 Sum of the angles of a pentagon is 540
What do you think about a hexagon? 4(180) = 720
SO . . . . . . . .
THEOREM
The sum of the measures of the INTERIOR angles with n sides is (n – 2)180
The sum of the measures of the exterior angles of any polygon is 360.
ALWAYS 360!!
TWAP—(TRY WITH A PARTNER) HINT: JUST PLUG INTO THE FORMULA! Find a) the sum of the interior angles and
b) the sum of the exterior angles for each shape
1) 32-gon 2) Decagon
Answers:1)a) 5400 b) 3602)a) 1440 b) 360
Other Formulas…
The measure of EACH EXTERIOR angle of a regular polygon is: 360
n(It’s 360 divided by the number of
sides)
The measure of EACH INTERIOR angle of a polygon is: (n-2)180 n
(It’s the SUM of Interior divided by # of sides)
Example
Find the measure of EACH interior angle of a polygon with 5 sides.
(5-2)180 53(180)=540540/5 = 108
EXAMPLE Find the measure of each interior angle of parallelogram RSTU.
Since the sum of the measures of the interior angles is
Step 1 Find the sum of the degrees!
EXAMPLE CONT.Sum of measures of interior angles
EXAMPLE CONTStep 2 Use the value of x to find the measure of each angle.
Answer: mR = 55, mS = 125, mT = 55, mU = 125
mR = 5x= 5(11)= 55
mS = 11x + 4= 11(11) + 4 = 125
mT = 5x= 5(11)= 55
mU = 11x + 4= 11(11) + 4 = 125
To Find # of sides…
Formula: ____360____ 1 ext. angle(360 divided by 1 ext angle)
Also: 1 interior angle + 1 exterior angle = 180
Example
How many sides does a regular polygon have if each exterior angle measures 45º?
360 45 n = 8 sides
EXAMPLE
How many sides does a regular polygon have if each interior angle measures 120º?
Find ext angle: 180-120= 60
360 60
n = 6 sides
EXAMPLE Find the value of x in the diagram.
How many degrees will it =?
Answer: x = 12
5x + (4x – 6) + (5x – 5) + (4x + 3) + (6x – 12) + (2x + 3) +
(5x + 5) = 360
(5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(–6) + (–5) + 3 + (–12) + 3 + 5] = 360
31x – 12 = 360
31x = 372
x = 12
EQUATIONS TO KNOW (FLASHCARDS!!!!)
Sum of interior angles
Each interior angle
Sum of exterior angles
Each exterior angle
# of Sides
2 180n
2 180n
n
360360
n360
1 .Ext
HOMEWORK
Pg. 398 #13-37 odd, 49