Posted by admin | Posted in Uncategorized | Posted on 24-07-2010
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Deg Regular
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| Football |
Geometry Question. i just don't get it!?
Find the Sum of the measures of the interior angles of the polygon belo.
22-gon
12-gon
15-gon
32-gon
For each regular polygon, find the measure of each exterior angle.
Quadrilateral
Nonagon
12-gon
Find the number of sides of a regular polygon having the given measure for each interior angle.
150 degress.
160 deg.
120 deg.
Find the number of sides of a polyon whose sum of the measures of tis interior angles is..
1980 deg.
2880 deg.
1260 deg.
Hopefully you know the definitions of "interior" and "exterior" angles and understand that they two are supplementary.
The sum of all the exterior angles of a closed geometric figure must be 360°. If there are n sides and angles in a regular "n-gon", Θ is the interior angle at each of the "n" vertices, n(180 - Θ) = 360 or
Θ = 180 - 360/n
Θ = 180(1-2/n)
and
the sum of the interior angles is ΣΘ = 180(n-2)
Now, you have all the information you need to answer those questions:
A: Sum of the interior angles of an n-gon = 180(n-2)
example: 22-gon = 180(22-2) = 20*180 = 3600°
B. Measure of each exterior angle of an n-gon = 360/n
example: Nonagon (n=9) = 360/9 = 40°
C. Number of sides of a regular polygon with a given interior angle = n = 360/ (180 - Θ)
example: 150° => n = 360/(180-150) = 360/30 = 12
D: Number of sides given the sum of interior angles: n = 2 + ΣΘ/180
example: ΣΘ = 1980 => n = 2 + 1980/180 = 11
There's all the formulae you need. Plug in your numbers, and you'll have your answers.
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