Download Chapter 6 – Polygons

Chapter 6 – Polygons
A _________________is a closed plane figure that is formed by 3 or more segments
called sides where each side intersects exactly 2 other sides, once at each endpoint
and no 2 sides with a common endpoint are collinear.
Each segment that forms a polygon is a __________. The common endpoint of 2
sides is a __________________. A segment that connects any 2 nonconsecutive
vertices is a _____________________.
# of sides
3
4
5
6
7
8
9
10
12
n
Name of polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
A polygon is equilateral if all its sides are  . It is equiangular if all its interior angles
are  . A polygon is ____________ if it is equilateral and equiangular. If a polygon is
not regular, it is called irregular.
A polygon is ____________ if any part of a diagonal contains points in the exterior of
the polygon. If no diagonal contains points in the exterior, then the polygon is
_______________. A regular polygon is always convex.
Ex. 1 Find the sum of the measures of the interior angles of a convex
nonagon.
(n – 2) ● 180
=
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Ex. 2 Find the measure of each interior angle of parallelogram RSTU.
Step 1
Find x.
Step 2
Use the value of x to find the measure of each angle.
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Ex. 3 A pottery mold makes bowls that are in the shape of a regular heptagon.
Find the measure of one of the interior angles of the bowl.
____________________________________________________________________
Ex. 4 Find the value of x in the diagram.
____________________________________________________________________
Ex. 5 The measure of an interior angle of a regular polygon is 144. Find the
number of sides in the polygon.
__________________________________________________________________
Ex. 6 Find the measure of each exterior angle of a regular pentagon.
YOU TRY!!!
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(Like Ex. 1) Find the sum of the measures of the interior angles of a convex
octagon.
____________________________________________________________________
(Like Ex. 2) Find the value of x.
____________________________________________________________________
(Like Ex. 4) Find the value of x in the diagram.
____________________________________________________________________
(Like Ex. 5) The measure of an interior angle of a regular polygon is 150. Find the
number of sides in the polygon. (Use the Interior Angle Sum Theorem to write
an equation to solve for n, the number of sides.)