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Math
A |
Each
Interior Angle of a Regular Polygon |
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First,
remember that the sum
of the interior
angles of a polygon is given by the formula
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Sum of
interior angles = 180(n-2) |
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A polygon is called a REGULAR
polygon when all of its sides are of the same length and all of
its angles are of the same measure. |
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The picture shown above is that
of a Regular
Pentagon. We know that to find the sum
of its interior angles we substitute n = 5
in the formula and get:
Since we know
that the pentagon is a regular
polygon, we know that the measure of each interior angle will be the
same. To find the size of each angle,
we just divide the sum (5400)
by the number
of angles
(which is the same as the number of sides).
5400
5 = 1080 |
The
number of degrees in each angle of a regular pentagon. |
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Look
at the pentagon to the right. Do angle E and angle B look
like they have the same measures? You're right --- they
don't. This pentagon is
not a
regular
pentagon.
If the angles of
a polygon do not
all
have the same measure, then we can't find the measure of any one
of them just by knowing their
sum. |
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Let's state
the general formula for finding each interior angle of a REGULAR polygon
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FORMULA:
Each interior angle of a regular
polygon =
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| 1. |
Find
the number of degrees in each interior angle of a regular
dodecagon. |
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It
is
a regular
polygon,
so we can use the formula. In a dodecagon, n =
12. |
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| 2. |
Each
interior angle of a regular polygon measures 1350. How
many sides does the polygon have ? |
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First,
set the formula (for each interior angle)
equal to the number of degrees given.
Cross multiply.
Multiply 180 by (n-2).
Subtract 180n from both sides of the equation.
Divide both sides of the equation by -45.
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