If each interior angle of a regular polygon is 150°, then it has _____ sides.

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Solution

The correct option is A
12

It is given that the polygon is regular. So all the sides and angles of the polygon are equal.

$∵$ exterior angle = 180° - interior angle

= 180° - 150°

= 30°

$∵$ Sum of exterior angles of any polygon = 360 $^{\circ}$

$\Rightarrow$ n $\times$ exterior angle = 360 $^{\circ}$ (where, n= Number of sides)

$\Rightarrow$ n = $\frac{360 °}{exterior angle}$

= $\frac{360 °}{30 °}$

= 12

$∴$ Number of sides = 12.

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