Final answer:
By using the Transitive property of equality to subtract the common measure of angle B from both sides of the given equation m∠A + m∠B = m∠B + m∠C, it is proven that m∠A is equal to m∠C, thereby showing the angles are congruent.
Step-by-step explanation:
To answer the question about proving that m∠C = m∠A using the given statement m∠A + m∠B = m∠B + m∠C, we first understand that the equation suggests there is a common measure m∠B on both sides. By subtraction, we can eliminate m∠B from both sides using the property that if two quantities are equal to the same quantity, then they are equal to each other (Transitive property of equality). So, subtracting m∠B from both sides gives us m∠A = m∠C. This shows that the measures of angles A and C are equal, which means the angles themselves are congruent. Therefore, option a) is the correct statement because "The angles are congruent, therefore, their measures are equal." This explanation provides sufficient proof for the given statement.