Download 360

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
2)a) 1440
b) 360
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
5
3(180)=540
540/5 = 108

EXAMPLE
Find the measure of each interior angle of
parallelogram RSTU.
Step 1 Find the sum of the degrees!
Since
angles is
the sum of the measures of the interior
EXAMPLE CONT.
Sum of measures
of interior angles
EXAMPLE CONT
Step 2 Use the value of x to find the measure of
each angle.
mR = 5x
= 5(11)= 55
mS = 11x + 4
= 11(11) + 4 = 125
mT = 5x
= 5(11)= 55
mU = 11x + 4
= 11(11) + 4 = 125
Answer: mR = 55, mS = 125, mT = 55,
mU = 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 =?
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
Answer:
x = 12
EQUATIONS TO KNOW (FLASHCARDS!!!!)

Sum of interior angles

Each interior angle
 n  2180
 n  2 180
n

Sum of exterior angles

Each exterior angle

# of Sides
360
1Ext.
360
360
n
HOMEWORK
 Pg.
398 #13-37 odd, 49