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In Exercises 3-6, find m∠1 and m∠2. Tell which theorem you use in each case. (See Example 1.) 3. 4. 5. 6....

In Exercises 3-6, find m∠1 and m∠2. Tell which theorem you use in each case. (See Example 1.)
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In Exercises 7-10, find the value of x. Show your steps. (See Examples 2 and 3.)
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In Exercises 11 and 12, find m∠1, m∠2, and m∠3. Explain your reasoning.
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13. ERROR ANALYSIS Describe and correct the error in the student's reasoning.

Answer

  1. 3. m∠1 = 63°, m∠2 = 117°. Theorem: Linear Pair Postulate.

  2. 4. m∠1 = 130°, m∠2 = 50°. Theorem: Linear Pair Postulate.

  3. 5. m∠1 = 122°, m∠2 = 58°. Theorem: Vertical Angles Theorem.

  4. 6. m∠1 = 40°, m∠2 = 140°. Theorem: Vertical Angles Theorem.

  5. 7. 2x = 128°; x = 64°. Steps: Set 2x equal to 128° because they are vertical angles.

  6. 8. 7x + 24 = 72°; 7x = 48°; x = 48/7. Steps: Set 7x + 24 equal to 72° because they are vertical angles.

  7. 9. 11x - 17 = 65°; 11x = 82°; x = 82/11. Steps: Set 11x - 17 equal to 65° because they are vertical angles.

  8. 10. 8x + 6 = 118°; 8x = 112°; x = 14. Steps: Set 8x + 6 equal to 118° because they are vertical angles.

  9. 11. m∠1 = 80°, m∠2 = 100°, m∠3 = 80°. Reasoning: Alternate Interior Angles Theorem and Linear Pair Postulate.

  10. 12. m∠1 = 47°, m∠2 = 133°, m∠3 = 47°. Reasoning: Alternate Interior Angles Theorem and Linear Pair Postulate.

  11. 13. The error is in assuming ∠9 ≅ ∠10 by the Corresponding Angles Theorem. The correct reasoning should use the Alternate Interior Angles Theorem.

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