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Answer :

Let the number of sides of a regular polygon be n.

We have, Sum of all interior angles = \((n – 2) \times 180^{\circ}\)

and, measure of its each angle=\(\frac{(n-2) \times 180^{\circ}}{n}\)

here we have each angle as \(165^{\circ}\)

\(\Rightarrow \frac{(n-2) \times 180^{\circ}}{n}=165\)

\(\Rightarrow 180n - 360 =165 n \quad \)[Cross multiplication and opening the brackets]

\(\Rightarrow 180n -165 n=360\)

\(\Rightarrow 15n = 360\)

\(\Rightarrow n = \frac{360}{15}=24\)

So, we have the number of sides of regular polygon as 24.

- 1.Find x in the following figures.
- 2.Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
- 3.How many sides does a regular polygon have if the measure of an exterior angle is \(24^{\circ}\)?
- 5.(a) Is it possible to have a regular polygon with measure of each exterior angle a is \(22^{\circ}\)? (b) Can it be an interior angle of a regular polygon? Why?
- 6.(a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?

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