Download 6. 8. exterior ∠ sum = sum of supplementary∠`s – interior ∠ sum

Exterior Angles
GEOMETRY
NAME_________________________
DATE __________ Per.___________
Polygons
that each interior/exterior angle pair
6. Note
of a polygon is supplementary.
interior ∠
regular
polygon # of ∠ ‘s exterior ∠ measure
triangle
3
square
pentagon
hexagon
octagon
decagon
exterior ∠
Use that information to calculate the exterior
angle measures and sums of each regular
polygon in the table at right.
a) Use the table in #6 to graph the exterior
angle sums of an n-sided regular polygon.
7.
e
x
t
e
r
i
o
r
900°
720°
540°
360°
180°
S
u
m
0°
1
2
3
4
5
6
7
8
9
10
3(120°)=360°
4(
)=
Use the table in #6 to graph the exterior angle
8. a)
measures of an n-sided regular polygon.
y
E
x
t
e
r
i
o
r
180 - 60 = 120°
exterior
∠ sum
x
∠
y
120°
100°
80°
60°
40°
20°
0°
1
# of sides of a regular n-sided polygon
2
3
4
5
6
7
8
9
10
x
# of sides of a regular n-sided polygon
b) Are the graphed points collinear?
c) What does the graph imply for n = 7 & 9?
b) Are the graphed points collinear?
d) Find an equation for the line through the pts.:
c) Is each quotient an exterior angle measure?
360÷3 =
360÷4 =
360÷5 =
e) Does this graph verify your guess in #5?
f) Should these plotted points be connected?
Why not?
9.
360÷6 =
360÷8 =
360÷10 =
d) Find a equation for the curve through the pts.:
(HINT: See part c)
Recall that adjacent interior/exterior angles are linear pairs. So, in a polygon with n-sides, there are also
____ vertices. Hence, there are also n pairs of _____________ angles. The sum of all of the
polygon’s supplementary angles is______, which is the sum of the interior and exterior ∠’s. Substitute
the formulas below to derive the exterior angle sum of any convex polygon.
exterior ∠ sum = sum of supplementary∠’s – interior ∠ sum
formula
(
) – ______( ___ – ___ )
exterior ∠ sum= =
=
10.
Show that:
180 −
180(n − 2) 360
=
n
n