To determine the number of sides in a regular polygon when given the measure of its exterior angle, we can use the formula: Exterior Angle = 360° / n,
where n represents the number of sides of the polygon. In this case, we know that the exterior angle is 24 degrees.
We can set up the equation:
24° = 360° / n
To find n, we can rearrange this equation:
n = 360° / 24°
Now, let’s perform the division:
n = 15
This means that the regular polygon has 15 sides.
In conclusion, a regular polygon with an exterior angle measuring 24 degrees is a 15-sided polygon, also known as a pentadecagon.