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Objectives

Objectives. Angle Pair Relationships Adjacent Angles Vertical Angles Linear Pair Complementary Angles Supplementary Angles. Adjacent angles are “side by side” and share a common ray. 15 º. 45 º. These are examples of adjacent angles. 45 º. 80 º. 35 º. 55 º. 130 º. 50 º. 85 º.

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Objectives

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  1. Objectives • Angle Pair Relationships • Adjacent Angles • Vertical Angles • Linear Pair • Complementary Angles • Supplementary Angles

  2. Adjacent angles are “side by side” and share a common ray. 15º 45º

  3. These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

  4. These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

  5. When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

  6. Vertical angles are opposite one another. 75º 105º 105º 75º

  7. Vertical angles are opposite one another. 75º 105º 105º 75º

  8. Vertical angles are congruent 150º 30º 150º 30º

  9. Supplementary angles add up to 180º. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Anglesbut not Adjacent

  10. Complementary angles add up to 90º. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Anglesbut not Adjacent

  11. Linear Pair Two adjacent angles (common vertex and a common ray) that form a straight line. So the two angles add up to ? 180

  12. Practice Time!

  13. Directions: Identify each pair of angles as vertical, supplementary, complementary, linear pair or none of the above.

  14. #1 120º 60º Supplementary Angles And a Linear Pair

  15. #2 60º 30º Complementary Angles

  16. #3 Vertical Angles 75º 75º

  17. #4 60º 40º None of the above

  18. #5 60º 60º Vertical Angles

  19. #6 135º 45º Supplementary Angles and a Linear Pair

  20. #7 25º 65º Complementary Angles

  21. #8 90º 50º None of the above

  22. Directions:Determine the missing angle.

  23. #1 ? 45º

  24. #1 135º 45º

  25. #2 65º

  26. #2 25º 65º

  27. #3 35º

  28. #3 35º 35º

  29. #4 ? 50º

  30. #4 130º 50º

  31. #5 ? 140º

  32. #5 140º 140º

  33. #6 Rectangle ? 40º

  34. #6 Rectangle 50º 40º

  35. ALGEBRA Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. Let x° be the measure of one angle. The measure of the other angle is 5x°. Then use the fact that the angles of a linear pair are supplementary to write an equation. EXAMPLE Find angle measures in a linear pair SOLUTION

  36. ANSWER The measures of the angles are 30° and 5(30)° = 150°. EXAMPLE Find angle measures in a linear pair x + 5x = 180° Write an equation. 6x = 180° Combine like terms. x = 30° Divide each side by 6.

  37. Find m< AEB 4x +8 6x - 42

  38. Write an equation & Solve

  39. Find the measure of each <

  40. Write an equation & Solve

  41. Homework Page 38 # 3 – 42 (x3) and 49 – 52 all Honors also: # 45, 55, & 56

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