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An
exterior angle of a polygon is
an angle that forms a linear pair with one of the angles of the
polygon.
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Two
exterior angles can be formed at each vertex of a polygon.
The exterior angle is formed by one side of the polygon and
the extension of the adjacent side. For the hexagon
shown at the left, <1 and <2 are exterior angles for that
vertex. Be careful, as <3 is NOT an exterior angle.
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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
formula uses only ONE exterior angle at each vertex. |
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Formula:
Sum exterior angles
of any
polygon = 360º
(using one exterior angle at a vertex) |
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Finding
the sum of the exterior
angles of a polygon is
simple. No matter what type of polygon you have, the sum
of the exterior angles is
ALWAYS
equal to
360º.
If you are working with a
regular polygon, you can determine the size
of EACH exterior angle by simply dividing the sum, 360, 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. |
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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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