Final answer:
To prove m∠C = m∠A, we observe that angle B's measurement can be subtracted from both sides of the given equation (m∠A + m∠B = m∠B + m∠C), thereby directly showing that m∠A equals m∠C.
Step-by-step explanation:
The statement given is m∠A + m∠B = m∠B + m∠C. To prove that m∠C = m∠A, we can start by looking at the properties of equality. Since addition is commutative, the order of the terms does not affect the sum. By applying this principle to the given equation, we can rearrange the terms to isolate the angles we are interested in comparing.
Given that the measure of angle B is on both sides of the equation, we can subtract m∠B from both sides. This leaves us with m∠A = m∠C, proving that the measure of angle C is equal to the measure of angle A. This straightforward approach is known as a paragraph proof, which uses written language to clearly explain the steps of the logical reasoning involved in proving a geometric statement.