8.1 Angle Measures in Polygons.notebook
March 02, 2010
Ch. 8 ­ Quadrilaterals
8.1 Find Angle Measures in Polygons
Polygon : Vertex : a closed plane figure with 3 or more sides.
the endpoint where to sides of a polygon intersect.
Number of sides
3
4
5
6
7
8
9
10
11
12
n
Type of polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Undecagon
Dodecagon
n­gon
8.1 Angle Measures in Polygons.notebook
March 02, 2010
diagonal (of a polygon): a segment that joins two
nonconsecutive vertices.
B
A
C
E
Polygon
Number of sides
D
Number of Triangles
Sum of interior angle measures
Triangle
3
1
1*180 = 180
Quadrilateral
4
2
Pentagon
5
3
2*180 = 360
3*180 = 540
Hexagon
6
4
4*180 = 720
(n‐2)
(n‐2)*180
.
.
.
n‐gon
n
8.1 Angle Measures in Polygons.notebook
Thm 8.1
March 02, 2010
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n‐gon is (n ‐ 2)*180
Corollary to Thm 8.1 ‐ Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a quadrilateral is 360o
D
A
C
B
m∠A + m∠B + m∠C + m∠D = 360o
3
8.1 Angle Measures in Polygons.notebook
March 02, 2010
Ex 1 Find the m∠F, m∠G and m∠H
G
H
x
m∠G = 550
measure of a quad = 360
x
55o
55 + x + 55 + x = 360
E
110 + 2x = 360
2x = 250
F
m∠H = m∠F = 125
x = 125
Ex 2
Find the sum of the measures of the interior
angles of a convex heptagon.
(7‐2)*180 = 5*180 = 900
Ex 3
The sum of the measures of the interior angles
of a convex polygon is 1080º. Classify the
polygon by the number of sides.
(n‐2)*180 = 1080
n‐2 = 1080
180
n‐2 = 6
4
n = 8
Homework
Pages 510–513 #1-10, 28, 29, 33, 34
8.1 Angle Measures in Polygons.notebook
Ex 4
March 02, 2010
Find the value of x in the diagram show.
110º
92º
xº
84º
100º
Q
Guided Practice:
1. Use the diagram at the right.
Find m∠S and m∠T
P
156º
93º
T
2. The measures of three of the interior angles of a
quadrilateral are 89º, 110º, and 46º. Find the measure
of the fourth interior angle.
R
85º
S
8.1 Angle Measures in Polygons.notebook
March 02, 2010
Bell Ringers ‐ March 3
Find the sum of the measures of the interior angles of the indicated convex polygon.
1. 16‐gon
2. 24‐gon
3. Find the value of x.
143
2x
4.
152
116
x
125
139
140
8.1 Angle Measures in Polygons.notebook
Thm 8.2
March 02, 2010
Polygon Exterior Angles Theorem
The sum of the measures of the exterior angles of a convex polygon, one at every vertex, is Ex 2 Find the value of y.
126
y
o
o
(y + 10)o
2yo
Ex 3 Find the value of x.
xo
Pages 510 - 513 # 13-15, 17-25, 30-32, 35-37, 39-41