Step 1 :Find the total age of all three people: \(kai_age + aron_age + grace_age = 12 + 16 + 17 = 45\)
Step 2 :Find the proportion of Aron's age to the total age: \(\frac{aron_age}{total_age} = \frac{16}{45} = 0.35555555555555557\)
Step 3 :Find the angle at the center of Aron's slice of cake: \(aron_proportion \times 360^\circ = 0.35555555555555557 \times 360^\circ = 128^\circ\)
Step 4 :\(\boxed{128^\circ}\)