I need help with my geometry hw, i need to now wat the properties are for the following statements.

1. If 2x=6, then x=3

2. If 42 degrees + measure of angle 2 = 90 degrees, then measure of angle 2 = 48 degrees

3. If measure of angle D = 40 degrees and measure of E = 90 degrees - measure of angle D, then measure of angle E is 50 degrees

4. If measure of J = 20 degrees,
then 3(measure of J) = 60 degrees

Please tell if my answers are correct or not
1. Substitution Property
2. Substitution Property
3. Substitution Property
4. Distributive Property

what is the ratio of the lengths of the corresponding sides

Your answers are almost correct. Let me explain why.

1. If 2x = 6, then x = 3.
This is an example of the Substitution Property of Equality. It states that if two expressions are equal to each other, then you can substitute one expression with the other in any equation or inequality. In this case, 2x is equal to 6, so you can substitute 2x with 6 and conclude that x is equal to 3. Therefore, your answer is correct.

2. If 42 degrees + measure of angle 2 = 90 degrees, then measure of angle 2 = 48 degrees.
This is also an example of the Substitution Property of Equality. You are given that the sum of 42 degrees and the measure of angle 2 is equal to 90 degrees. By subtracting 42 degrees from both sides of the equation, you can conclude that the measure of angle 2 is 48 degrees. Therefore, your answer is correct.

3. If measure of angle D = 40 degrees and measure of E = 90 degrees - measure of angle D, then measure of angle E is 50 degrees.
Although you correctly used the Substitution Property in the previous examples, in this case, it's not applicable. Instead, this statement demonstrates the Property of Supplementary Angles. The Property of Supplementary Angles states that if two angles are supplementary (their measures add up to 180 degrees), then the value of one angle can be determined by subtracting the measure of the other angle from 180 degrees. In this case, the measure of angle E is given as 90 degrees minus the measure of angle D, which equals 90 - 40 = 50 degrees. Therefore, your answer is incorrect.

4. If measure of J = 20 degrees, then 3(measure of J) = 60 degrees.
This statement demonstrates the Distributive Property, which states that multiplying a number by the sum of two other numbers is the same as multiplying the number by each of the two numbers and then adding the results. In this case, if the measure of angle J is given as 20 degrees, then 3 times the measure of angle J is 3 * 20 = 60 degrees. Therefore, your answer is correct.

To summarize:

1. Correct! The Substitution Property of Equality is applicable.
2. Correct! The Substitution Property of Equality is applicable.
3. Incorrect. This is an example of the Property of Supplementary Angles.
4. Correct! This is an example of the Distributive Property.