Question

If the sum of the interior angles of a regular polygon is 2 160˚, how many sides does it have? Show all the steps of your calculation.

Answer 1

Answer:

14 sides

Step-by-step explanation:

Using the formula, (n-2)× 180 = 2160

n-2 = $\frac{2160}{180}$ = 12

n= 12+2 = 14

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Answer 2

Each interior angle of regular polygon = (n-2)×180°

n

160° = (n-2)×180°

n

160n = 180n - 360°

160n - 180n = - 360°

- 20n = - 360°

n = -360°/-20

n = 16

Hence the polygon has 16 sides.