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Questions and Answers
What theorem justifies the statement that ∠2 ≅ ∠3 in the second proof?
What theorem justifies the statement that ∠2 ≅ ∠3 in the second proof?
Which property is used when concluding that 5x = 80 in the second proof?
Which property is used when concluding that 5x = 80 in the second proof?
What is the value of m∠1 in the third proof if x = 9?
What is the value of m∠1 in the third proof if x = 9?
Which step employs the transitive property in the first proof?
Which step employs the transitive property in the first proof?
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What conclusion can be drawn from m∠QRS = 75° and the angle addition postulate in the second proof?
What conclusion can be drawn from m∠QRS = 75° and the angle addition postulate in the second proof?
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Study Notes
Angle Proofs - Practice Problems
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Problem 1: Given ∠1 ≅ ∠2 and m∠1 = m∠3, prove m∠1 = m∠3.
- Statements: 1. ∠1 ≅ ∠2, 2. ∠2 ≅ ∠3, 3. ∠1 ≅ ∠3, 4. m∠1 = m∠3
- Reasons: 1. Given, 2. Given, 3. Transitive Property of Congruence, 4. Definition of Congruent Angles
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Problem 2: Given T is in the interior of ∠QRS, m∠QRS = 75°, m∠QRT = (3x - 1)°, and m∠TRS = (2x - 4)°, find x.
- Statements: 1. T is in the interior of ∠QRS, 2. m∠QRT + m∠TRS = m∠QRS, 3. m∠QRS = 75°, 4. m∠QRT = (3x - 1)°, 5. m∠TRS = (2x - 4)°, 6. (3x - 1) + (2x - 4) = 75, 7. 5x - 5 = 75, 8. 5x = 80, 9. x = 16
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Problem 3: Given ∠1 and ∠2 form a linear pair, m∠1 = (15x + 9)°, and m∠2 = (4x)°, find x.
- Statements: 1. ∠1 and ∠2 form a linear pair, 2. ∠1 and ∠2 are supplementary, 3. m∠1 + m∠2 = 180°, 4. m∠1 = (15x + 9)°, 5. m∠2 = (4x)°, 6. (15x + 9) + (4x) = 180°, 7. 19x + 9 = 180, 8. 19x = 171, 9. x = 9
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Description
Test your understanding of angle proofs through a series of practice problems. This quiz includes various scenarios involving congruent angles, finding unknown variables, and applying properties related to angle measures. Sharpen your proof skills and reinforce your knowledge in geometry.
