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Q.

If one of the interior angles of a regular polygon is equal to $\frac{5}{6}$ times of one of the interior angles of a regular pentagon, then the number of sides of the polygon is

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a

2^{2}

b

6

c

3

d

4

answer is B, D.

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Detailed Solution

One of interior angles of a regular polygon

= \frac{5}{6}

one of the interior angle of regular pentagon

$\frac{(n - 2) 180 °}{n} = \frac{5}{6} . \frac{(5 - 2) 180 °}{5}$

$\frac{(n - 2) 180 °}{n} = \frac{3 \times 30 °}{1}$

$180 ° n - 360 ° = 90 ° n$

$180 ° n - 90 ° n = 360 °$

$90 ° n = 360 °$

$∴$ Sides of polygon $n = 4$

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