Question

3. Consider an N sided regular polygon whose interior angles measured in degrees are
natural numbers. What is maximum possible value of N.
Report sum of digits of N.​

Answer 1

Given :   an N sided regular polygon whose interior angles measured in degrees are natural numbers

To find :  maximum possible value of N. and sum of digits of N

Solution:

interior angles of regular polygon  = (n - 2)(180)/n

n = number of Sides of polygon

= 180  -  360/n

n = 360 is the maximum value which will give integral output

n = 360

Angle = 179°

maximum possible value of N. = 360

Sum of Digits = 3 +6 + 0 = 9

9 is the sum of digits of N sided regular polygon whose interior angles measured in degrees are

natural numbers.

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29 Apr 2020 ... regular Pentagon =(n-2)×180°)/n.