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# Simple angle problem

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In a certain regular polygon, the measure of each interior angle is 12 times the measure of each exterior angle. Find the number of sides in this regular polygon.

May 10, 2020

#1
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If I knew the value of an angle I could work backwards from (n – 2) • 180.

To obtain the value of an angle, I'm going to have to divide 180 by 13.

That division doesn't come out even, so I'm stuck there.  Sorry.

May 10, 2020
#2
#3
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Let's try it out.

Using (n – 2) x 180o we find the sum of all 36 angles  =   6,120o

Since it's a regular polygon each of the 36 angles must equal 6,120o / 30  =   170o

This leaves only 10o for the external angle.  That doesn't have the required 12 to 1 ratio.

Have I made a mistake somewhere?  What say you?

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Guest May 12, 2020
#4
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Jeeze, I swear I proofread it a dozen times before publishing.  And yet, this....

The line should be

Since it's a regular polygon each of the 36 angles must equal 6,120o / 36  =  170o

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Guest May 12, 2020