We know that in the given design all of the small arcs around the circle are congruent. We want to find the measure of each of the small arcs. Since the arcs are congruent, they have equal measure. Let's call the measure of each of these arcs α.
We can see that the 8 angles of measure α make a complete angle. Therefore, 8 times α is 360^(∘).
8 * α = 360 ^(∘) ⇔ α = 45^(∘)
The measure of each of the small arcs is 45^(∘).
