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Exercise

Exercise. Classify a 90° angle according to its measure. right. Exercise. Classify a 45° angle according to its measure. acute. Exercise. Classify a 120° angle according to its measure. obtuse. Exercise. Solve c + 57 = 90. c = 33. Exercise. Solve s + 63 = 180. s = 117. A. F.

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Exercise

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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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