m∠2 + m∠3 + m∠4 = 180°/ reason: Given?
m∠1 + m∠2 = 180°/reason: Supplementary Angle definition
m∠1 + m∠2 = m∠2 + m∠3 + m∠4/reason: Substitution property equality
m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 -m∠2/reason= Subtraction property equality
m∠1 = m∠3 + m∠4/reason: simplify
Please check? I'm not sure about 1&5
1. The statement "m∠2 + m∠3 + m∠4 = 180°" is a valid equation. It states that the sum of angles 2, 3, and 4 is equal to 180 degrees. However, the reason is not given. It could be an assumption made based on the context of the problem or a previous theorem or property that justifies this equation.
2. The statement "m∠1 + m∠2 = 180°" is justifiable based on the definition of supplementary angles. Two angles are considered supplementary when their sum equals 180 degrees.
3. The statement "m∠1 + m∠2 = m∠2 + m∠3 + m∠4" is justified using the substitution property of equality. This property allows you to replace an equal value with another equal value in an equation. In this case, m∠2 is being replaced by itself.
4. The statement "m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 - m∠2" is justified using the subtraction property of equality. It states that if you subtract the same value from both sides of an equation, the equation remains true. In this case, m∠2 is being subtracted from both sides.
5. The statement "m∠1 = m∠3 + m∠4" is not correct. The previous steps do not lead to this conclusion. To simplify the equation, you would only need to combine like terms, not remove a term from one side.
Based on the given statements, the correct equation would be "m∠1 + m∠2 = m∠3 + m∠4," which states that the sum of angles 1 and 2 is equal to the sum of angles 3 and 4.