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Understanding Angles: Classification, Complementary and Supplementary Concepts

This resource provides a thorough understanding of angles, including their classification into right, acute, and obtuse based on their measures. It also covers complementary and supplementary angles, with clear examples and solutions to equations involving angle measures. The concepts of adjacent, vertical, and parallel angles, along with transversals and their interactions, are explained. Engaging exercises help reinforce understanding of angle measures and relationships in geometry.

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Understanding Angles: Classification, Complementary and Supplementary Concepts

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  1. Exercise Classify a 90° angle according to its measure. right

  2. Exercise Classify a 45° angle according to its measure. acute

  3. Exercise Classify a 120° angle according to its measure. obtuse

  4. Exercise Solve c + 57 = 90. c = 33

  5. Exercise Solve s + 63 = 180. s = 117

  6. A F D C B E

  7. P R Q M N O

  8. Complementary • Two angles whose measures add up to 90° are complementary.

  9. Supplementary • Two angles whose measures add up to 180° are supplementary.

  10. Example 1 Write and solve an equation to find the supplement of 38°. Let s = the supplement. s + 38 = 180 s + 38 – 38 = 180 – 38 s = 142° The supplement of a 38° angle is a 142° angle.

  11. B A C D

  12. Adjacent angles—have a common vertex and a common ray between them. • Intersecting lines—share a common point.

  13. l A m

  14. Vertical Angles • Vertical angles are two angles with no sides in common formed by intersecting lines.

  15. Example 2 Without measuring, find the measure of 3, 4, and 5. 3 50° 6 5 4

  16. m 3 m 4 m 5 3 50° 6 5 4 = 130° = 130° = 50°

  17. " " • Perpendicular lines intersect to form right angles.

  18. Example 3 Without measuring, find m 1, m 2, and m 3. 3 2 36° 1

  19. m 1 m 2 m 3 3 2 36° 1 = 36° = 90° = 54°

  20. Parallel Lines • Parallel lines are lines in the same plane that do not intersect.

  21. Transversal • A transversal is a line that intersects two or more other lines.

  22. A E B C D F

  23. Alternate Interior Angles m 3 = m 6 m 4 = m 5 t 1 2 r 3 4 5 6 s 7 8

  24. Alternate Exterior Angles m 1 = m 8 m 2 = m 7 t 1 2 r 3 4 5 6 s 7 8

  25. Corresponding Angles m 1 = m 5 m 3 = m 7 m 2 = m 6 m 4 = m 8 t 1 2 r 3 4 5 6 s 7 8

  26. Example 4 Line a is parallel to line b. Use the figure to identify the following angles.

  27. 10 6 a 9 5 8 4 b 7 3 4 9 and are alternate interior angles.

  28. 10 6 a 9 5 8 4 b 7 3 6 7 and are alternate exterior angles.

  29. 10 6 a 9 5 8 4 b 7 3 8 10 and are corresponding angles.

  30. 10 6 a 9 5 8 4 b 7 3 5 3 and are corresponding angles.

  31. Example 5 Assuming the two lines are parallel and cut by a transversal, find the measure of 1, 2, 3, and 4.

  32. m 1 m 2 m 3 m 4 1 2 110° 3 4 = 110° = 70° = 110° = 110°

  33. Exercise Given parallel lines a and b are cut by transversal tand m 1 = 143°, find the measure of each angle without measuring.

  34. m 6 5 4 6 a 3 7 8 1 2 b = 37°

  35. m 8 5 4 6 a 3 7 8 1 2 b = 53°

  36. m 5 5 4 6 a 3 7 8 1 2 b = 53°

  37. m 3 5 4 6 a 3 7 8 1 2 b = 37°

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