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

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) (Show Source): You can put this solution on YOUR website!
One interior angle of a polygon is found by the equation:
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.
--------------------------

Multiply both sides by n

Multiply the 180 through of the right side.

Get all the n terms on one side of the equation by subtracting 180n from both sides.

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Now plug 156 into the equation for A.

Combine like terms.

Divide both sides by -24.

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Follow the same steps for the rest of the given angles.
For A = 157.5

----------------------------
For A = 162

I will leave the rest up to you.

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