given: (mangle a + mangle b=mangle b + mangle c) prove: (mangle c = mangle a) write a paragraph proof to…

Explanation:

Step1: Start with given equation

We are given (m\angle A + m\angle B=m\angle B + m\angle C).

Step2: Subtract (m\angle B) from both sides

By the subtraction - property of equality, ((m\angle A + m\angle B)-m\angle B=(m\angle B + m\angle C)-m\angle B). Simplifying the left - hand side gives (m\angle A+(m\angle B - m\angle B)=m\angle A), and simplifying the right - hand side gives ((m\angle B - m\angle B)+m\angle C=m\angle C). So, (m\angle A = m\angle C).

Answer:

We are given (m\angle A + m\angle B=m\angle B + m\angle C). By the subtraction property of equality, if we subtract (m\angle B) from both sides of the equation ((m\angle A + m\angle B)-m\angle B=(m\angle B + m\angle C)-m\angle B). The left - hand side simplifies to (m\angle A) since (m\angle B - m\angle B = 0), and the right - hand side simplifies to (m\angle C) for the same reason. Thus, we have proven that (m\angle C=m\angle A).