How many sides does a regular polygon have, if the measure of an exterior angle is $24^{\circ}$ ?

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Solution

Let the number of sides of the polygon be n.
Sum of exterior angles of a regular polygon $= 360^{\circ}$
Hence, the number of sides
$= \frac{S u m o f e x t e r i o r a n g l e s}{E a c h i n t e r i o r a n g l e} = \frac{360^{\circ}}{24} = 15$
Hence, the regular polygon has 15 sides.

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