Question

If each interior angle of a regular polygon is 175 degree. Find the number of sides of the polygon .

Answer 1

Answer: A regular polygon with each interior angle of 175 deg will have each exterior angle as 180–175 = 5 deg. Hence the number of sides in the regular polygon = 360/5 = 72 sides.

Step-by-step explanation:

Answer 2

Answer:

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$each \: interior \: angle \: of \: the \: regular \: polygon = 175degree \\ each \: interior \: angle \: of \: the \: regular \: polygon = \frac{n - 2}{n} = 180degree \\ 175degree = \frac{n - 2}{n} \times 180degree \\ 175n = 180n - 360 \\ 360 = 180n - 175n \\ 360 = 5n \\ n = \frac{360}{5} \\ n = 72 \\ number \: of \: sides \: in \: the \: regular \: polygon \: is \: 72$

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