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# Angle relationships

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### Angle relationships

1. 1. Angle Relationships & Parallel Lines Pre-Algebra
2. 2. Adjacent angles are “side by side” and share a common ray. 15º 45º
3. 3. These are examples of adjacent angles. 80º 45º 35º 55º 130º 50º 85º 20º
4. 4. These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º
5. 5. Complementary Angles sum to 90° 50° 40°
6. 6. Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Complementary Angles Angles but not Adjacent
7. 7. Supplementary Angles sum to 180° 30° 150°
8. 8. Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Supplementary Angles Angles but not Adjacent
9. 9. Vertical Angles are opposite one another.Vertical angles are congruent. 100° 100°
10. 10. Vertical Angles are opposite one another.Vertical angles are congruent. 80° 80°
11. 11. Lines l and m are parallel. l||m Note the 4 angles that measure 120°. 120° 120° l 120° 120° mLine n is a transversal. n
12. 12. Lines l and m are parallel. l||m Note the 4 angles that measure 60°. 60° 60° l 60° 60° mLine n is a transversal. n
13. 13. Lines l and m are parallel. l||mThere are many There are 4 pairs ofpairs of angles that angles that areare supplementary. vertical. 60° 120° 120° 60° l 60° 120° 120° 60° m Line n is a transversal. n
14. 14. If two lines are intersected by a transversaland any of the angle pairs shown below arecongruent, then the lines are parallel. Thisfact is used in the construction of parallellines.
15. 15. Practice Time!
16. 16. 1) Find the missing angle. ?° 36°
17. 17. 1) Find the missing angle. ?° 36° 90 ° – 36 = 54°
18. 18. 2) Find the missing angle. ?° 64°
19. 19. 2) Find the missing angle. ?° 64° 90 ° – 64° = 26°
20. 20. 3) Solve for x. 2x° 3x°
21. 21. 3) Solve for x. 2x° 3x° 3x° + 2x° = 90° 5x = 90 x =18
22. 22. 4) Solve for x. x + 25 2x + 5
23. 23. 4) Solve for x. x + 25 2x + 5 (2x + 5) + (x + 25) = 90 3x + 30 = 90 3x = 60 x = 20
24. 24. 5) Find the missing angle. ?° 168°
25. 25. 5) Find the missing angle. ?° 168° 180° – 168° = 12°
26. 26. 6) Find the missing angle. 58° ?°
27. 27. 6) Find the missing angle. 58° ?° 180° – 58° = 122°
28. 28. 7) Solve for x. 4x 5x
29. 29. 7) Solve for x. 4x 5x 4x + 5x = 180 9x = 180 x = 20
30. 30. 8) Solve for x. 2x + 10 3x + 20
31. 31. 8) Solve for x. 2x + 10 3x + 20 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30
32. 32. 9) Lines l and m are parallel. l||m Find the missing angles. 42° a° c° b° l d° e° g° f° m
33. 33. 9) Lines l and m are parallel. l||m Find the missing angles. 42° 138° 138° 42° l 42° 138° 138° 42° m
34. 34. 10) Lines l and m are parallel. l||m Find the missing angles. 81° a° c° b° l d° e° g° f° m
35. 35. 10) Lines l and m are parallel. l||m Find the missing angles. 81° 99° 99° 81° l 81° 99° 99° 81° m
36. 36. 11) Find the missing angles. 70 ° 70 ° b°Hint: The 3 angles in atriangle sum to 180°. d° 65 °
37. 37. 11) Find the missing angles. 70 ° 70 ° 40°Hint: The 3 angles in atriangle sum to 180°. 75 ° 65 °
38. 38. 12) Find the missing angles. 45 ° 50 ° b°Hint: The 3 angles in atriangle sum to 180°. d° 75 °
39. 39. 12) Find the missing angles. 45 ° 50 ° 85°Hint: The 3 angles in atriangle sum to 180°. 20° 75 °
40. 40. In the figure a || b.13. Name the angles congruent to ∠3. ∠1, ∠5, ∠714. Name all the angles supplementary to ∠6. ∠1, ∠3, ∠5, ∠715. If m∠1 = 105° what is m∠3? 105°16. If m∠5 = 120° what is m∠2? 60°
41. 41. The End