Question

Exterior angle of a
regular polygon is 24 degree . find the number of side of the polygon.

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Answer 1

Correct Question:

Exterior angle of a regular polygon is 24 degree . find the number of side of the polygon.

Answer

Let us take the side be x

As we know the sum of exterior angles of regular polygon = 360 °.

$\implies\sf {number \: of \: sides \: = \frac{sum \: of \: exterior \: angles}{each \: interior \: angle \: } }$

= 360 °/ 24°

$\implies\sf{15}$

Hence, the regular polygon has 15 sides .

☆Additional Information ☆

Regular polygon -  a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Answer 2

Given :-

• exterior angle of regular polygon = 24°

To find :-

• No. of sides in the polygon

Knowledge required :-

The formula for finding measure of the exterior angle of any regular polygon is $\bf{\dfrac{360}{n}}$ where n is the no. of sides in the polygon.

Solution :-

Let, no. of sides in the polygon = n

Since , the formula for finding the measure of the exterior angle of any regular polygon is $\bf{\dfrac{360}{n}}$  , where n is the no. of sides .

therefore,

$\longmapsto\;\;\bf{24=\dfrac{360}{n}}\\\\\longmapsto\bf{24 n = 360}\\\\\longmapsto\bf{n=\dfrac{360}{24}}\\\\\longmapsto \overbrace{\underbrace{\large{\red{\bf {\;\;\;n=15\;\;\;}}}}}$

Hence, the polygon have 15 sides.

$\rule{205}1$

Supplementary Knowledge

⇢ A polygon having all sides and all angles equal is called  a regular polygon.

⇢ When , there are n sides in a polygon  then ,

sum of all interior angles of polygon will be given by (n - 2)180°.

⇢ The sum of the exterior angles of a convex polygon is always 360°, no matter how many sides are there in the polygon.

$\rule{205}1$