In a regular nonagon, each interior angle measures 140 degrees (since the sum of interior angles in any polygon is given by (n-2) * 180 degrees, where n is the number of sides of the polygon).
To determine the smallest degree measure for a regular nonagon to rotate onto itself, we need to find the smallest value of k (where k is a positive integer) such that 140 degrees multiplied by k is divisible by 360 degrees (a full rotation).
By calculating the successive multiples of 140 degrees, we find:
140 degrees * 1 = 140 degrees (not divisible by 360)
140 degrees * 2 = 280 degrees (not divisible by 360)
140 degrees * 3 = 420 degrees (divisible by 360)
Therefore, the smallest degree measure for a regular nonagon to rotate onto itself is 420 degrees.
What is the smallest degree measure for a regular nonagon to rotate onto itself?
1 answer
1 answer