Question

The measure of each exterior angle of a regular polygon is 6°. Find the number of sides of the polygon.

Answer 1

now let its sum of angles is 360

n x 6 = 360

n = 60 sides

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Answer 2

Answer:

45 sides

Step-by-step explanation:

let the number of sides of the polygon be x.

measure of each exterior side of the polygon = 6°

$\therefore$

measure of each interior angle = (180 - 6)° = 172°

Now,

A/Q,$\: \: \frac{180(x - 2)}{x} = 172$

$\implies 180x - 360 = 172x$

$\implies 180x - 172x = 360$

$\implies (180 - 172)x = 360$

$\implies 8x = 360$

$\implies x = \frac{360}{8}$

$\implies x = \frac{8 \times 45}{8}$

$\implies x = \frac{1 \times 45}{1}$

$\implies x = 45$

Hence, there are 45 sides in the given regular polygon.