Mysterious Polygon

The sum of all external angles in any polygon is 360 degrees.

If the polygon is regular, then all the external angles will be equal.

Here it is given that all external angles are equal and equal to 24 degrees.

So, $24n = 360 \longrightarrow n = 15$ , where $n$ is the number of sides of the polygon.

Since each exterior angles are equal, It is Regular polygon, Number of sides = 360/24 = 15

sum of angles of polygon = 180(n-2) where n is the no of sides . for each exterior angle 24 each interior angle = (180-24)=156 ; total sum of angles for n sided polygon = 156n ; equating 180(n-2) = 156n ; n=15 ans

For an n-sided polygon measure of external angle = 360/n therefore 360/n= 24 Implies n= 15