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POLYGONS
10/17/2007
EQ: How do I find the measure of an interior & exterior angle of a
polygon?
POLYGONS
10/17/2007
What does the word “polygon” mean?
What is the smallest number of
sides a polygon can have?
What is the largest number of
sides a polygon can have?
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Hexagon
Dodecagon
Heptagon
n-gon
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Important Terms
A VERTEX is
the point of
intersection of
two sides
F
A segment whose
endpoints are two
nonconsecutive
vertices is called
a DIAGONAL.
A
B
CONSECUTIVE
VERTICES are two
endpoints of any side.
C
E
D
Sides that share a
vertex are called
CONSECUTIVE
SIDES.
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
More Important Terms
EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
REVIEW:
What is the sum of the measures of the
interior angles of a triangle?
180°
180°
180°
What is the sum of the measures of the
interior angles of any quadrilateral?
360°
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
If a convex polygon has n sides,
then the sum of the measure of the
interior angles is
(n-2)(180°)
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Ex. 1 Use the regular pentagon to answer the
questions.
A) Find the sum of the
measures of the
interior angles.
540°
B) Find the measure of
ONE interior angle
108°
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Two more important terms
Interior
Angles
Exterior
Angles
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
If any convex
polygon, the sum of
the measures of the
exterior angles, one at
each vertex, is 360°.
2
1
3
5
4

m1  m2  m3  m4  m5  360
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
If any convex
polygon, the sum of
the measures of the
exterior angles, one at
each vertex, is 360°.
1
3
2

m1  m2  m3  360
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Ex. 2 Find the measure of ONE exterior angle of a
regular hexagon.
sum of the exterior angles

number of sides

360

6
60°
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Ex. 3 Find the measure of ONE exterior angle of a
regular heptagon.
sum of the exterior angles

number of sides

360

7
51.4°
EQ: How do I find the measure of an interior & exterior angle of a
Ex. 4 The sum of the measures of five
interior angles of a hexagon is 535. What
is the measure of the sixth angle?
POLYGONS
10/17/2007
185°
EQ: How do I find the measure of an interior & exterior angle of a
Ex. 5 The measure of the exterior angle
of a quadrilateral are x, 3x, 5x, and 3x.
Find the measure of each angle.
POLYGONS
10/17/2007
30°, 90°, 150°, and 30°
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
Ex. 6 The sum of the interior angles of a
polygon is 720. Find the number of sides.
n=6
EQ: How do I find the measure of an interior & exterior angle of a
POLYGONS
10/17/2007
EQ: How do I find the measure of an interior & exterior angle of a