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
If m∠1+m∠2=180∘ and m∠2+m∠3=180∘, which statement is always true?
1. m∠2 + m∠3 + m∠4 = 180°/ reason: Given?
Well, if that's what you were given, I guess we have to believe it. But maybe the angles are just having a party and decided to add up to 180°. Who knows?
2. m∠1 + m∠2 = 180°/reason: Supplementary Angle definition
Ah, yes, the good ol' supplementary angles. They add up to 180°, just like cookies and milk. Together, they make the perfect combo.
3. m∠1 + m∠2 = m∠2 + m∠3 + m∠4/reason: Substitution property equality
Substitution, substitution, huh? Sounds like a fancy word for swapping. It's like exchanging your fries for someone else's nachos. But in this case, we're just replacing one angle with another.
4. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 - m∠2/reason: Subtraction property equality
Ah, the subtraction property equality! It's like when you borrow a pencil from your friend and then return it immediately. Hey, at least you're being fair.
5. m∠1 = m∠3 + m∠4/reason: Simplify
Well if you simplify things enough, you might end up with just a single angle on the left side. It's like when you have a big bowl of soup and keep taking out some liquid until you're left with just one drop. Mmm... angle soup!
Let's go through each step to check your reasoning:
1. m∠2 + m∠3 + m∠4 = 180°/ reason: Given?
This step is correct. It is given that the sum of angles 2, 3, and 4 is equal to 180°.
2. m∠1 + m∠2 = 180°/ reason: Supplementary Angle definition
This step is correct. It is a property of supplementary angles that the sum of two angles is equal to 180°.
3. m∠1 + m∠2 = m∠2 + m∠3 + m∠4/reason: Substitution property equality
This step is correct. By substituting the value of 180° (from step 2) for m∠1 + m∠2, you can rewrite the equation.
4. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 - m∠2/reason: Subtraction property equality
This step is correct. By subtracting m∠2 from both sides, the equation remains balanced.
5. m∠1 = m∠3 + m∠4/reason: simplify
This step is not correct. Subtracting m∠2 from both sides in step 4 results in m∠1 = m∠3 + m∠4, not the notation m∠1 + m∠2 = m∠3 + m∠4. The subtraction property of equality allows you to remove terms on both sides of the equation.
So, step 5 should be: m∠1 = m∠3 + m∠4/reason: simplify
Overall, your reasoning is correct except for step 5.
Let's go through each step to verify them:
1. m∠2 + m∠3 + m∠4 = 180° / Given?
This step is correct. The reason given is that it is given in the problem statement.
2. m∠1 + m∠2 = 180° / Supplementary Angle definition
This step is also correct. The reason given is the definition of supplementary angles, which states that if two angles add up to 180 degrees, they are supplementary.
3. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 / Substitution property equality
This step is correct. The reason given is the substitution property of equality, which allows us to replace one expression with another that is equal to it.
4. m∠1 + m∠2 - m∠2 = m∠2 + m∠3 + m∠4 - m∠2 / Subtraction property of equality
This step is incorrect. The subtraction property of equality states that if you subtract the same quantity from both sides of an equation, the equality is still maintained. In this case, we cannot subtract m∠2 from both sides because it is not canceled out. Therefore, this step should not be included.
5. m∠1 = m∠3 + m∠4 / Simplify
This step is correct. The reason given is to simplify the equation by combining like terms. Here, we have canceled out the m∠2 term on both sides, leaving us with m∠1 on one side and m∠3 + m∠4 on the other side.
To summarize, step 1 and step 3 are correct, step 2 is correct, step 4 is incorrect, and step 5 is correct.