Regular Polygons

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Regular Polygons

• Lesson 7.4 Recognize regular polygons.
• Use formulas to find measure of an exterior angle
  of an equiangular polygon.

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Define regular polygon
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Regular PolygonsEquilateral and equiangular
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• Theorem 58 The measure E of each exterior angle
  of an equiangular polygon of n sides is given by
  the formula
• E 360

n
5
Find m?1 in the figure below
m?1 360
5
m?1 72?
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Theorem 58 The measure E of each exterior angle
of an equiangular polygon of n sides is given by
the formula E 360
n
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Problem 1
1. How many degrees in each exterior ? of an
equiangular heptagon?
E 360
7
51 3/7?
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Problem 2
2. If the exterior angle of a polygon is 18?,
how many sides does the polygon have?
E 360
n
18 360
Plug in 18 for E
n
18n 360
Multiply both sides by n
n 20 sides
Divide by 18
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Problem 3
3. If each angle of a polygon is 108?, how many
sides does it have?
First find the exterior angle. 180º - 108º 72º
Set up with correct formula E 360
72n 360 n 5 The polygon has 5 sides.
n
9
Problem 4
4. Given the stop sign shown, is ?NTE scalene,
isosceles, equilateral or undetermined?
O
I
T
Isosceles
N
S
Q
E
U