SOLUTION: Find the number of sides of a regular polygon given the measure of an interior angle: 1. 156 degrees 2. 157.5 degrees 3. 162 degrees 4. 144 degrees 5. 165 degrees 6. 140 degr

Algebra ->  Polygons -> SOLUTION: Find the number of sides of a regular polygon given the measure of an interior angle: 1. 156 degrees 2. 157.5 degrees 3. 162 degrees 4. 144 degrees 5. 165 degrees 6. 140 degr      Log On


   

Question 762659: Find the number of sides of a regular polygon given the measure of an interior angle:
1. 156 degrees
2. 157.5 degrees
3. 162 degrees
4. 144 degrees
5. 165 degrees
6. 140 degrees
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
One interior angle of a polygon is found by the equation: A+=+%28%28n-2%29%2A180%29%2Fn
Where n is the number of sides of the polygon.
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I will help you answer the first few.
You are one given the angle of 156
Plug 156 into the equation for A.
Since you will be doing this calulations multiple times, we will simplify the equation.
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A+=+%28%28n-2%29%2A180%29%2Fn
Multiply both sides by n
A%2An+=+%28n-2%29%2A180
Multiply the 180 through of the right side.
A%2An+=+180n+-+360
Get all the n terms on one side of the equation by subtracting 180n from both sides.
A%2An+-+180n+=+-360
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Now plug 156 into the equation for A.
A%2An+-+180n+=+-360
%28156%29%2An+-+180n+=+-360
Combine like terms.
-24n+=+-360
Divide both sides by -24.
highlight%28n+=+15%29
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Follow the same steps for the rest of the given angles.
For A = 157.5
A%2An+-+180n+=+-360
157.5%2An+-+180n+=+-360
-22.4n+=+-360
highlight_green%28n+=+16%29
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For A = 162
A%2An+-+180n+=+-360
162%2An+-+180n+=+-360
-18n+=+-360
highlight%28n+=+20%29
I will leave the rest up to you.