Download Lesson 5.1 Polygon Sum Conjecture notes

5.1 Polygon Sum Conjecture
Investigation: Measure all of the interior angles of each polygon, then find each sum.
No. of sides
Sum of meas. of
angles
3
4
5
6
7
8
…
n
Quadrilateral Sum Conjecture
The sum of the measures of the four angles of any quadrilateral is ______.
Pentagon Sum Conjecture
The sum of the measures of the five angles of any pentagon is _______.
Polygon Sum Conjecture
The sum of the measures of the n interior angles of an n-gon is _____________ .
Geometry Lesson 5.1: Polygon Sum Conjecture
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Example 1: Use the Polygon Sum Conjecture to find the sum of the interior angles of each polygon.
a. undecagon
b. 15-gon
c. 25-gon
d. 50-gon
Example 2: Find the measure of each missing angle.
105
139
110
101
120
106
121
b
c
65
46
a
100
80
b
133
Geometry Lesson 5.1: Polygon Sum Conjecture
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Example 3: Find the number of sides of each polygon with the following interior angle sums.
a. 3240
b. 10440
c. 4860
d. 5580
Example 4: How many triangles are formed by drawing diagonals from one vertex in each polygon? What
is the sum of the measures of the angles in each polygon?
Geometry Lesson 5.1: Polygon Sum Conjecture
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Example 5: Determine the measure of each angle.
B
C
2x - 5
2x + 1
2x - 1 A
D
2x - 9
2x - 6
E
mA = _______
mB = _______
mC = _______
mD = _______
mE = _______
mJ = _______
M
L
3x - 4
4x - 2
N
7x - 2
K 2x + 1
2x + 4 F
J
5x + 5
4x - 3
7x + 6
I
x-5
G
H
mF = _______
mG = _______
mH = _______
mI = _______
mK = _______
mL = _______
mM = _______
mN = _______
Homework: pp. 257 – 259 => 1 – 14; 18; 20 - 21
Geometry Lesson 5.1: Polygon Sum Conjecture
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