Question

Given: m∠A+mB=mB+mC
Prove: mC=mA

Answer 1

Given:
`\(m\angle A + m\angle B = m\angle B + m\angle C\)`

Prove:
`\(m\angle C = m\angle A`

Step-by-step explanation:

The given expression
`\(m\angle A + m\angle B = m\angle B + m\angle C\)` suggests that the measure of angle \(A\) combined with the measure of angle B is equal to the sum of the measures of angles B and C.

By subtracting
`\(m\angle A = m\angle C\`)from both sides of the equation, we get
`\(m\angle A = m\angle C\)`, which implies that the measure of angle Cis equal to the measure of angle \(A\).

In conclusion, the statement is proven, and we can now assert that
`\(m\angle C = m\angle A\)`. This deduction is based on the assumption that the sum of the measures of angles A and B is equal to the sum of the measures of anglesB and C. The algebraic manipulation establishes the equality of
`\(m\angle C\) and \(m\angle A\).`

Answer 2

By subtracting m∠B from both sides of the given equation m∠A + m∠B = m∠B + m∠C, we can prove that m∠C = m∠A, indicating angle A and angle C have equal measures.

Step-by-step explanation:

The question is asking to prove that if m∠A + m∠B = m∠B + m∠C, then it must be that m∠C = m∠A. To solve this, we can manipulate the given equation. Starting with the given, we subtract m∠B from both sides to isolate the variables m∠A and m∠C on each side of the equation, which gives us m∠A = m∠C. This proves that the measures of angle C and angle A are equal.