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Adjacent, vertical, complementary and supplementary angles

Adjacent, vertical, complementary and supplementary angles. Mr. Peterson. CC standard 7.g.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simples equations for an unknown angle in a figure. Paraphrase:

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Adjacent, vertical, complementary and supplementary angles

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  1. Adjacent, vertical, complementary and supplementary angles Mr. Peterson

  2. CC standard 7.g.5Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simples equations for an unknown angle in a figure. • Paraphrase: • Identify adjacent and vertical angels. • Find angel measures using adjacent and vertical angles. • Classify pairs of angles as complementary, supplementary, or neither. • Find angle measures using complementary and supplementary angles.

  3. Input • Vertex - Endpoint where two line segments or lines come together. • Adjacent angles – Angles that share a common side and have the same vertex. • Vertical angles – Opposite angles formed by the intersection of two lines. • Congruent angles – Angles that have the same measure. • Complementary angles – Two angles whose sum of their measure is 90°. • Supplementary angles - Two angles whose sum of their measure is 180°.

  4. Types of Angles Acute - Obtuse - Angles that measure less than 90°. Angles that measure more than 90° and less than 180°. Right - Straight - Angles that measure exactly 90°. Angles that measure exactly 180°.

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

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

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

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

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

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

  11. Vertical angles are congruent (equal). 150º 30º 150º 30º

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

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

  14. Guided PracticeDirections: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

  15. #1 120º 60º

  16. #1 120º 60º Supplementary Angles

  17. #2 60º 30º

  18. #2 60º 30º Complementary Angles

  19. #3 75º 75º

  20. #3 Vertical Angles 75º 75º

  21. #4 60º 40º

  22. #4 60º 40º None of the above

  23. #5 60º 60º

  24. #5 60º 60º Vertical Angles

  25. #6 135º 45º

  26. #6 135º 45º Supplementary Angles

  27. #7 25º 65º

  28. #7 25º 65º Complementary Angles

  29. #8 90º 50º

  30. #8 90º 50º None of the above

  31. 100 80 80 100 90 70 110 110 70 120 60 60 120 130 50 50 130 140 40 40 140 150 30 30 150 160 20 20 160 170 10 10 170 Protractor work: Guided Practice • 1. Draw a straight line.

  32. 100 80 80 100 90 70 110 110 70 120 60 60 120 130 50 50 130 140 40 40 140 150 30 30 150 160 20 20 160 170 10 10 170 Protractor work: Guided Practice • 2. Draw a ray to form an angle of 40°from the right side.

  33. Protractor work: Guided Practice • 3. Find the measure of the angle supplementary to the angle you just created. 40° 140°

  34. Protractor work: Guided Practice • 4. Use a straightedge to extend the ray you drew to below the line. 40° 140°

  35. Protractor work: Guided Practice • 5. What is the measure of angle X? 40° 140° x y 40° 140° Why? Angle Y? How did you find the answer?

  36. Time for you to try some on your own

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