Tag: exterior angles of a polygon

Questions Related to exterior angles of a polygon

How many sides does a regular polygon have if the measure of an exterior angle is $24^{0}$?

maths polygons exterior angles of polygon sum of exterior angles of polygons exterior angles of a polygon

  1. $14$

  2. $13$

  3. $15$

  4. $18$

Show answer
Correct Option: C
Explanation:

Here, let the number of sides of the polygon be $n$ 

So, the number of exterior angles is $n$ 
Since it is a regular polygon, each exterior angles are equal to one another.
$ \therefore$ The sum of the exterior angles $={ 360 }^{ o }$
$ \therefore$  Each angle $=\theta =\dfrac { { 360 }^{ o } }{ n }$ 
$\Longrightarrow n=\dfrac { { 360 }^{ o } }{ \theta  } $ 
Here $\theta ={ 24 }^{ o } $ 
$ \therefore  n=\dfrac { { 360 }^{ o } }{ { 24 }^{ o } } =15$
Hence, the answer is $15$.