Question

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
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.