Question

given: (mangle a + mangle b=mangle b + mangle c). prove: (mangle c = mangle a). write a paragraph proof to prove the statement.

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, if we subtract \(m\angle B\) from the left - hand side and the right - hand side of the equation, we get \((m\angle A + m\angle B)-m\angle B=(m\angle B + m\angle C)-m\angle B\).

Step3: Simplify both sides

On the left - hand side, \(m\angle A+(m\angle B - m\angle B)=m\angle A\), and on the right - hand side, \((m\angle B - m\angle B)+m\angle C=m\angle C\). So, \(m\angle C = m\angle A\).

Answer:

We are given \(m\angle A + m\angle B=m\angle B + m\angle C\). By the subtraction property of equality, we can subtract \(m\angle B\) from both sides of the equation. On the left - hand side, \((m\angle A + m\angle B)-m\angle B=m\angle A+(m\angle B - m\angle B)=m\angle A\), and on the right - hand side, \((m\angle B + m\angle C)-m\angle B=(m\angle B - m\angle B)+m\angle C=m\angle C\). Thus, we have proven that \(m\angle C = m\angle A\).