Answer: each time the pentagon is rotated 72, it maps back onto itself. There are five values of a for which the pentagon maps back onto itself. this is the same as the number of sides of the pentagon.
Step-by-step explanation: edmentum
A regular pentagon has 5 congruent sides and a measure of 360 degrees, at its center.
Pentagon ABCDE and A'B'C'D'E coincide at 4 values of (a)
The angle where pentagon ABCDE and pentagon A'B'C'D'E coincide is:
[tex]\mathbf{\theta = \frac{360}{5}}[/tex]
[tex]\mathbf{\theta = 72}[/tex]
Other angles between 0 and 360 degrees, where pentagon ABCDE and pentagon A'B'C'D'E coincide are multiples of 72.
So, we have:
[tex]\mathbf{a = 72^o,\ 144^o,\ 216^o,\ 288^o}[/tex]
The count of angles is 4
Hence, pentagon ABCDE and A'B'C'D'E coincide at 4 values of (a)
Read more about transformations at:
https://brainly.com/question/15158635
