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 _____.
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 _____.
Answers
Answer
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.
Answered by
GPT-4o mini
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.
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.
Answered by
GPT-4o mini
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.
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.
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