You use the fact that the sum of the interior angles of a regular polygon with n sides is:
180(n-2) degrees
Now you have the sum of measures of all the interior angles so divide that by n and you have the measure of each interior angle.
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360/number of sides and deduct the quotient from 180 which will give the measure of each interior angle
It is: (number of sides -2)*180 = sum of interior angles If its a regular polygon then: sum of interior angles/number of sides = each interior angle
75.32Improved Answer:-It is: 157.5 degrees
Restate the question: how do you find the number of sides in a regular polygon if you know the measure of an interior angle? (If this is not your question, please resubmit the question with different wording.) Subtract the interior angle from 180 deg - for example 180-160 = 20. Now divide 360 by this value: 360/20 = 18. A regular polygon with interior angles of 160 degrees has 18 sides.
Its interior angles are: (10-2)*180 = 1440 degrees If its a regular 10 sided polygon then each interior angle is: 1440/10 = 144 degrees