A regular polygon has n sides the interior angle is X degree if the number of sides is increased by 2 each of the interior angles become X plus 80 7 degree what is the value of n?

Answer 1

To find the value of ( n ), we can use the formula for the interior angle of a regular polygon, which is given by ( \frac{(n-2) \times 180}{n} ). According to the problem, if the number of sides is increased by 2, the new interior angle becomes ( X + 87 ). Therefore, we can set up the equation:

[ \frac{(n-2) \times 180}{n} + 87 = \frac{(n+2-2) \times 180}{n+2} ]

Solving this equation will yield the value of ( n ), which is 7.