Drag and drop the reasons to match the statements into the correct location to complete the proof. Given: Angles 1 and 2 are a linear pair. Prove that x = 11

Question

1) Angles 1 and 2 are a linear pair. Given. 2) Angles 1 and 2 are supplementary. Linear pair postulate. 3) m∠1 + m∠2 = 180° _____. 4) 11x - 6 + 4x + 21 = 180 _____. 5) 15x + 15 = 180 _____. 6) 15x = 165 _____. 7) x = 11 _____.

Answer 1

To complete the proof, we can organize the statements and the reasons corresponding to each:

1. Statement: Angles 1 and 2 are a linear pair.
   Reason: Given.

2. Statement: Angles 1 and 2 are supplementary.
   Reason: Linear pair postulate.

3. Statement: m∠1 + m∠2 = 180°.
   Reason: Definition of supplementary angles.

4. Statement: 11x - 6 + 4x + 21 = 180.
   Reason: Substitution (substituting angle measures).

5. Statement: 15x + 15 = 180.
   Reason: Combining like terms.

6. Statement: 15x = 165.
   Reason: Subtracting 15 from both sides.

7. Statement: x = 11.
   Reason: Dividing by 15.

This arrangement shows the logical flow of the proof that concludes with proving that \( x = 11 \) based on the provided steps and reasoning.

Answer 2

Options you can use to fill in the blank are, combine like terms, definition of supplementary angles, substitution, division property of equality, subtraction property of equality.

Answer 3

Based on the options provided, here’s how the statements and reasons can be matched to complete the proof:

1. Statement: Angles 1 and 2 are a linear pair.
   Reason: Given.

2. Statement: Angles 1 and 2 are supplementary.
   Reason: Linear pair postulate.

3. Statement: m∠1 + m∠2 = 180°.
   Reason: Definition of supplementary angles.

4. Statement: 11x - 6 + 4x + 21 = 180.
   Reason: Substitution.

5. Statement: 15x + 15 = 180.
   Reason: Combine like terms.

6. Statement: 15x = 165.
   Reason: Subtraction property of equality.

7. Statement: x = 11.
   Reason: Division property of equality.

This arrangement fills in the blanks appropriately using the options you provided.