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Math
A |
Exterior
Angles |
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An
exterior
angle of a polygon is formed by
extending one
side of the polygon. |
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In the
diagram to the left, angle 1 is an exterior
angle of polygon ABCDEF. It was formed by extending side ED to a
point Y.
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Note: While it is
possible to draw TWO (equal) exterior angles at each
vertex of a polygon, the sum of the exterior angles
uses only ONE exterior angle at each vertex. |
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Finding
the sum of the exterior
angles of a polygon is
simple. No matter what type of polygon we have, the sum
of the exterior angles is
ALWAYS
equal to 360º. |
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Formula:
Sum exterior angles =
360º |
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Since all
the angles in a regular polygon are
equal in measure, to find the measure of each exterior angle
of a regular
polygon we just divide 360º by the number of angles.
Remember,
the formula below will ONLY work in a regular
polygon. |
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Formula: Each exterior angle (regular
polygon) =
 |
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| 1. |
Find
the sum of the exterior angles of:
| a) |
a
pentagon |
Answer:
3600 |
| b) |
a
decagon |
Answer:
3600 |
| c) |
a
15 sided polygon |
Answer:
3600 |
| d) |
a
7 sided polygon |
Answer:
3600 |
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| 2. |
Find
the measure of each exterior angle of a regular hexagon. |
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A
hexagon has 6 sides, so n = 6
Substitute in the formula. |
3600
 6
=
600
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| 3. |
The
measure of each exterior angle of a regular polygon is
45º.
How many sides does the polygon have ? |
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Set
the formula equal to 450.
Cross multiply and solve for n.
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=
450 |
45n
= 360
n = 8
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