If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
(1 point)
Responses
24
24
12
12
15
15
18
18
To find the number of sides in a regular polygon when given the measure of an exterior angle, we can use the formula:
Interior angle = 180 - Exterior angle
Given that the measure of the exterior angle is 24, we can find the measure of the interior angle:
Interior angle = 180 - 24
Interior angle = 156
In a regular polygon, all interior angles are equal. Let's denote the number of sides in the polygon as n. We can use the formula for the sum of interior angles in a polygon:
Sum of interior angles = (n - 2) * 180
Since all interior angles are equal, each interior angle is equal to the sum of the interior angles divided by the number of sides:
Interior angle = (n - 2) * 180 / n
Setting this equal to 156, we can solve for n:
(n - 2) * 180 / n = 156
Now, let's solve the equation:
180n - 360 = 156n
180n - 156n = 360
24n = 360
n = 360 / 24
n = 15
Therefore, the polygon has 15 sides.
To find the number of sides of a regular polygon given the measure of an exterior angle, you can use the formula:
Number of sides = 360° / Measure of exterior angle.
In this case, the measure of the exterior angle is given as 24°.
So, to find the number of sides, we can substitute this value into the formula:
Number of sides = 360° / 24° = 15.
Therefore, the polygon has 15 sides.