# Free Answer: Given: m∠a + m∠b = m∠b + m∠c prove: m∠c = m∠a write a paragraph proof to prove the statement.

Given: m∠a + m∠b = m∠b + m∠c prove: m∠c = m∠a write a paragraph proof to prove the statement. You will find answers to all your questions about this subject in this content. I wish you pleasant reading.

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## Given: m∠a + m∠b = m∠b + m∠c prove: m∠c = m∠a write a paragraph proof to prove the statement.

Given: m∠a + m∠b = m∠b + m∠c prove: m∠c = m∠a write a paragraph proof to prove the statement.

Here’s a paragraph proof for the given statement: Given that m∠a + m∠b = m∠b + m∠c, we want to prove that m∠c = m∠a. We can start by simplifying the left-hand side of the equation using the associative property of addition: m∠a + m∠b = (m∠b + m∠a) + m∠c. Since m∠b + m∠a = m∠a + m∠b, we can substitute this equality in to get m∠a + m∠b = m∠a + m∠b + m∠c. Now we can cancel out the common terms on both sides of the equation, leaving us with m∠c = m∠a, which is exactly what we wanted to prove.

To further explain this proof, we can use the fact that the sum of angles in a triangle is always 180 degrees. If we let a, b, and c be the angles of the triangle, then we know that m∠a + m∠b + m∠c = 180. Since m∠a + m∠b = m∠b + m∠c, we can substitute this into the equation to get m∠a + m∠b + m∠b + m∠c = 180. Simplifying this, we get m∠a + 2m∠b + m∠c = 180.

But we also know that m∠a + m∠b + m∠c = 180, so subtracting this equation from the previous one gives us m∠b = 0. This means that b is a zero degree angle, which implies that a and c must be equal. Therefore, we have proven that m∠c = m∠a.