If each exterior angle of a regular polygon measures 40 degrees, what is the total number of sides in the polygon?
a.) 9
b.) 8
c.) 6
d.) 5
The sum of the exterior angles of a polygon is 360 degrees
Let the number of sides be n
360/n = 40
40n = 360
n = 9
To solve this problem, we can use the fact that the sum of all exterior angles of a polygon is always 360 degrees.
Let's assume that the regular polygon has n sides. Since each exterior angle measures 40 degrees, we can write the equation:
40 * n = 360
To find the value of n, we need to solve this equation. Dividing both sides by 40 gives:
n = 360 / 40
Simplifying the right side gives:
n = 9
Therefore, the regular polygon has 9 sides.
So, the answer is (a) 9.
In a regular polygon, all the exterior angles are equal.
Given that each exterior angle of the regular polygon measures 40 degrees, we can find the total number of sides by dividing 360 degrees (the sum of all exterior angles in a polygon) by the measure of each exterior angle.
360 degrees / 40 degrees = 9
Therefore, the total number of sides in the polygon is 9.
The correct answer is a.) 9.