Kai, Aron and Grace share the same birthday. They cut their shared birthday cake into three slices with sizes proportional to their ages. What is the angle, in degrees $\left(^{\circ}\right)$, at the centre of Aron's slice of cake?
Kai is 12 years old Aron is 16 years old Grace is 17 years old

Answer

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Answer

$\boxed{128^\circ}$

Steps

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 ：$\boxed{128^\circ}$