Final answer:
By using the commutative property of addition and the properties of equality, we can rearrange the given equation to show that mZC equals MZA, proving the student's statement.
Step-by-step explanation:
The student is given that MZA + MZB = MZB + MZC. To prove that mZC = MZA, we will use properties of equality and the commutative property of addition which says A + B = B + A. Since MZB is on both sides of the equation, it can be subtracted from both sides resulting in MZA = MZC.
This is analogous to the basic arithmetic principle that if A + B = B + C, then A = C. The same logic applies here to angles. Therefore, by simple algebraic manipulation and using properties of angle addition, we have proven that mZC = MZA.