Question

if a regular polygon, each interior angle is 170 degree then how much number of sides it has ?
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Answer 1

Question :- Find the number of Sides of a regular polygon if each interior angle measures 170 Degree.

Solution :-

Each interior angle of a regular Polygon :- 180 - Exterior angle.

170 = 180 - $\frac{360}{n}$

$\frac{360}{n}$ = 180 - 170

$\frac{360}{n}$ = 10 Degree

$\frac{360}{n}$ or n = 36.

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Alternate Methos :-

Each interior angle of regular polygon = $\frac{(n-2)×180}{n}$

170 = $\frac{(n-2)×180}{n}$

170n = 180n -360

360 = 180n - 360

360 = 10n

$\frac{360}{10}$ = n

n = 36