Download Lesson 5.2 Exterior Angles of a Polygon notes

5.2 Exterior Angles of a Polygon
Investigation: Measure each of the exterior angles of each polygon, then find each sum.
No. of sides
Sum of exterior
angle measures
3
4
5
6
7
8
…
n
Exterior Angle Sum Conjecture
For any polygon, the sum of the measures of a set of exterior angles is _______.
Equiangular Exterior Angle Conjecture
For any regular polygon, the measure of each exterior angle is __________.
Equiangular Polygon Conjecture
The measure of each interior angle of a regular n-gon is __________________ or __________________.
Example 1: What is the sum of the exterior angles of each polygon?
a)
Octagon
b)
15-gon
c)
50-gon
Geometry Lesson 5.2: Exterior Angles of a Polygon
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Example 2: Find each lettered angle measure.
a
b
Example 3: Find the measure of each missing exterior angle.
48
71
58
67
91
90
43
a
a
46
Geometry Lesson 5.2: Exterior Angles of a Polygon
b
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Example 4: What is the measure of each i) interior angle and ii) exterior angle of each regular polygon?
a)
Hexagon
i)
ii)
b)
Octagon
i)
ii)
c)
18-gon
i)
ii)
d)
20-gon
i)
ii)
Geometry Lesson 5.2: Exterior Angles of a Polygon
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Example 5: How many sides does each regular polygon have if each exterior angle measures the
following?
a) 12
b) 40
c) 36
d) 8
Example 6: How many sides does each regular polygon have if each interior angle measures the
following?
a) 144
b) 108
c) 156
d) 170
Geometry Lesson 5.2: Exterior Angles of a Polygon
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Example 7: Find the given angle in each.
a) A pentagon has exterior angle measures of 65°, 69°, 68°, and 78°. What is the measure of the
fifth interior angle?
b) A hexagon has exterior angle measures of 55°, 61°, 67°, 66°, and 58°. What is the measure of
the sixth interior angle?
c) A pentagon has exterior angle measures of 79°, 66°, 64°, and 77°. What is the measure of the
fifth interior angle?
Geometry Lesson 5.2: Exterior Angles of a Polygon
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Example 8: Find x and y.
a) x = _________
y = __________
c) x = _________
y = __________
b) x = _________
y = __________
Homework: pp. 262 – 263 => 1 – 11; 13 - 16
Geometry Lesson 5.2: Exterior Angles of a Polygon
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