Question

If exterior angle of regular polygon is one-Fifth of its interior angle find number of sides of polygon

Answer 1

Let the interior angle be x

Exterior angle will be (180 - x)

(180 - x) = 1x / 5

5(180 - x) = x

900 - 5x = x

900 = x + 5x

900 = 6x

x = 900 / 6

x = 150

Now each interior angle is 150 degrees

Then the number of sides are

{n - 2) * 180 } / n = 150

(n - 2 ) * 180 = 150n

n - 2 = 150n / 180

n - 2 = 5n/6

6(n - 2) = 5n

6n - 12 = 5n

6n - 5n = 12

n = 12

The number of sides are 12.

Answer 2

let interior angle is x
so exterior angle will be x/5
as we know

interior angle + exterior angle in regular polygon = 180°
so
$x + \frac{x}{5} = 180 \\ \frac{5x + x}{5} = 180 \\ \frac{6x}{5} = 180 \\ \\ x = 150$
so interior angle of this polygon is 150°
we know
interior angle for regular polygon = (n-2)*180/n where n is no. of side
so

150 = (n-2)*180/n
$\frac{5}{6} = \frac{n - 2}{n} \\ 5n = 6n - 12 \\ n = 12$
so sides of regular polygon is 12

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