if the measure of an exterior angle of a regular polygon is 24 how many sides does the polygon have
The measure of an exterior angle of a regular polygon is equal to 360 degrees divided by the number of sides in the polygon.
In this case, we can set up an equation:
360/n = 24
Multiply both sides of the equation by n:
360 = 24n
Divide both sides of the equation by 24:
n = 360/24
Simplify:
n = 15
Therefore, the polygon has 15 sides.
The measure of each exterior angle of a regular polygon can be found using the formula:
Exterior angle = 360 degrees / number of sides
Given that the measure of the exterior angle is 24 degrees, we can set up the equation:
24 degrees = 360 degrees / number of sides
To find the number of sides, we can rearrange the equation:
number of sides = 360 degrees / 24 degrees
Simplifying:
number of sides = 15
Therefore, the regular polygon has 15 sides.
To find the number of sides in a regular polygon, we can use the formula:
Number of sides = 360 degrees ÷ Measure of each exterior angle
In this case, if the measure of an exterior angle is given as 24 degrees, we can substitute that into our formula:
Number of sides = 360 degrees ÷ 24 degrees
Now, we can perform the division:
Number of sides = 15
Therefore, the regular polygon has 15 sides.