Question 4
How many sides does a regular polygon have if each of its interior angles is $165^{\circ}$ ?

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Solution

Let number of sides be n.
Exterior angle $= 180^{\circ} - 165^{\circ} = 15^{\circ}$
Sum of exterior angles of a regular polygon $= 360^{\circ}$
Hence, the number of sides
$= \frac{S u m o f e x t e r i o r a n g l e s}{E a c h e x t e r i o r a n g l e} = \frac{360^{\circ}}{15} = 24$
Hence, the regular polygon has 24 sides.

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How many sides does a regular polygon have if each of its interior angles is 165°?

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