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Understanding Angle Relationships: Supplementary and Corresponding Angles Explained

In this comprehensive overview, Mrs. Rivas explores various angle relationships, including same-side interior angles, corresponding angles, and alternate exterior angles. Key problems involving linear pairs and the properties of supplementary angles are presented, illustrating how to solve for unknown variables in angle measures. The step-by-step solutions nurture understanding of foundational concepts in geometry, aiding students in their learning journey. Join Mrs. Rivas as she simplifies the complexities of angle relationships in a clear and engaging manner.

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Understanding Angle Relationships: Supplementary and Corresponding Angles Explained

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  1. Mrs. Rivas

  2. Mrs. Rivas

  3. Mrs. Rivas

  4. Mrs. Rivas

  5. Mrs. Rivas

  6. Mrs. Rivas Same-side Interior angles 103 (x − 26) + x = 180 x − 26 + x = 180 77 2x − 26 = 180 2x = 206 x = 103 103 + 77 = 180

  7. Mrs. Rivas Corresponding angles (3x − 5) = (x + 55) 3x − 5 = x + 55 2x − 5 = 55 2x = 60 x = 30 3(30) − 5 = 30 + 55 90 − 5 = 30 + 55 85 = 85

  8. Mrs. Rivas Linear Pair angles = Suppl. (x + 20) + (x + 10) = 180 95 85 x + 20 + x + 10 = 180 2x + 30 = 180 2x = 150 x = 75 95 + 85 = 180

  9. Mrs. Rivas Linear Pair angles = Suppl. (y − 40) + y = 180 110 y − 40 + y = 180 2y − 40 = 180 70 2x = 220 x = 110 110 + 70 = 180

  10. Mrs. Rivas Alternate Exterior angles (2x + 6) = 42 42 2x + 6 = 42 2x = 36 x = 18

  11. Mrs. Rivas Same-side Interior angles (3x − 17) + 98 = 180 82 3x − 17 + 98 = 180 3x + 81 = 180 3x = 99 x = 33 98 + 82 = 180

  12. Mrs. Rivas Same-side Interior angles (2x + 20) + (6x + 24) = 180 54 2x + 20 + 6x + 24 = 180 8x + 44 = 180 126 8x = 136 126 + 54 = 180 x = 17

  13. Mrs. Rivas Alternate Exterior angles 132 (2x + 2) = (3x − 63) 2x + 2 = 3x − 63 2x = 3x − 65 − x = − 65 132 x = 65

  14. Mrs. Rivas Linear Pair angles = Suppl. (5x − 5) + 140 = 180 5x − 5 + 140 = 180 40 5x + 135 = 180 5x = 45 140 + 40 = 180 x = 9

  15. Mrs. Rivas Same-side Interior angles 68 (4x − 8) + 112 = 180 4x − 8 + 112 = 180 4x + 104 = 180 4x = 76 x = 19 112 + 68 = 180

  16. Mrs. Rivas 140 15. 40 Linear Pair angles = Suppl. (7x + 14) + (2x + 4) = 180 7x + 14 + 2x + 4 = 180 140 + 40 = 180 9x + 18 = 180 9x = 162 x = 18

  17. Mrs. Rivas 127 16. 53 Linear Pair angles = Suppl. (4x − 5) + (x + 20) = 180 4x − 5 + x + 20 = 180 127 + 53 = 180 5x + 15 = 180 5x = 165 x = 33

  18. Mrs. Rivas Algebra Determine the value of for which . Then find and . 17. Alternate exterior Angles are

  19. Mrs. Rivas Algebra Determine the value of for which . Then find and . 18. Alternate exterior Angles are

  20. Mrs. Rivas 19. Developing Proof Complete the flow proof below. Given: 1 and 4 are supplementary. Prove: ∠2 and∠3aresupplementary Given Converse of same-side Interior Angles Vertical ∠s are ≅

  21. Mrs. Rivas 20. Developing Proof Complete the flow proof below. Given: and are supplementary; Prove: ∠2 and∠3aresupplementary ∠s suppl. to the same ∠ are ≅ ∠1 ≅∠4 If corr. ∠s are ≅ lines are Give

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