Question

Sum of the external angles of a regular polygon is 1/6th of the sum of the interior angles. Find the number of sides.

Answer 1

Answer:

14 sides

Step-by-step explanation:

For any polygon, sum of external angles is 360°.

So let sum of internal angles is x°.

$\frac{360}{x} = \frac{1}{6}$

$x = 360 \times 6 = {2160}^{0}$

So x = 2160°.

Now for any polygon with n sides, sum of internal angles is

$(n - 2)180$

so,

$(n - 2)180 = 2160 \\ = > n - 2 = \frac{2160}{180} = 12 \\ = > n = 12 + 2 = 14$

So the polygon has 14 sides.

Answer 2

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