Download Geometry Section 7.1 Angles of Polygons

Geometry Section 7.1
Angles of Polygons
What you will learn:
1. Use the interior angles measures of
polygons
2. Use the exterior angles measures of
polygon
The word polygon means many sides. In
simple terms, a polygon is a many sided
closed figure.
When naming a polygon, you must list the
vertices in order either clockwise of
counterclockwise.
The polygon at the right could be named
ABCDEF
BAFEDC
A diagonal of a polygon is a segment joining
two nonadjacent vertices.
A polygon is equilateral iff all its sidesa re
congruent.
A polygon is equiangular iff all its angles are
congruent.
A polygon that is both equilateral and
equiangular is called a ________
regular polygon.
A polygon is convex iff no line containing a
side contains a point in the interior of the
polygon.
A polygon that is not convex is _________.
concave
Convex
Concave
triangle
hexagon
nonagon
n - gon
quadrilateral
heptagon
decagon
pentagon
octagon
dodecagon
Example: How many diagonals can be drawn from one vertex
in a hexagon?
Always three less than
the number of sides
Example: How many total diagonals can be drawn in a
hexagon?
a heptagon?
4  4  3  2  1  14
3  3  2 1  9
4
5
6
n
2
3
4
n2
360
540
720
180(n  2)
Theorem 7.1: Polygon Interior Angles Theorem
The sum of the measures of the interior angles of
a (convex) polygon with n sides is ____________
(n  2)180
Corollary 7.1: Corollary to the Polygon Interior
Angles Theorem
The sum of the measures of the interior angles of
a quadrilateral is ___________
360
(12  2)180
10 180  1800
(20  2)180
18 180  3240
3240
 162
20
While the sum of the interior angles of a polygon
changes as the number of sides changes, this is
not the case with the sum of the exterior angles.
Theorem 7.2: Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles of
a convex polygon, one at each vertex, is ______
360
180
180
180
180
180
900
540
360
(5  2)180
3 180
(n  2)180
(n  2)180
n
(16  2)180 2520
 157.5
2520
16
22
3600
 163. 6 3
22
360
360
360
360
360
(n  2)180  3600
360
n
360
 22.5
16
360
 16. 3 6
22
(n  2)180
(n  2)180
n
(16  2)180 2520
 157.5
2520
16
22
3600
 163. 6 3
22
(25  2)180 4140
 165.6
25
4140
360
 25
14.4
(30  2)180
360
 30
5040
12
360
360
360
360
n
360
 22.5
16
360
 16. 3 6
22
360
360
180  168 
12
360 / n  14.4
HW: pp 364 – 365 / 4 – 30 Even, 38, 40, 41