Question

How many sides are regular polygon if each interior angle measures of 165°?

Answer 1

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Q. Find the number of sides of a regular polygon if each interior angle of the polygon is 165°.

Solution:-

Let n be the number of sides of the polygon.

Each interior angle of a regular polygon= (n-2)×180/n
=> (n-2)×180/n=165° i.e. (n-2)×180°=165×n
=> 180n-360=165n
=> 180n-165n=360
=> 15n=360
=> n= 360÷15
=> n= 24

Hence the polygon has 24 sides.

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Answer 2

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