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ANGLES
<ul><li>An  angle  (  ) is formed by two rays (called  sides  of the angle) with the same endpoint (called the  vertex  of...
CLASSIFICATION OF ANGLES (according to measure) <ul><li>x o </li></ul><ul><li>ACUTE  x o   x o </li></ul><ul><li>0 < x < 9...
PROTRACTOR POSTULATE <ul><li>Let OA and OB be opposite rays in a plane.  OA, OB and all the rays with endpoint O that can ...
ANGLE ADDITION POSTULATE <ul><li>If point B   is in the interior of   AOC, then  </li></ul><ul><li>m  AOB + m  BOC = m ...
Angle Pairs <ul><li>Two coplanar angles are  adjacent  if and only if they satisfy three conditions: </li></ul><ul><ul><li...
<ul><li>Two angles are  complementary  if and only if the sum of their measures is equal to 90 o .  Each angle is the  com...
<ul><li>Find the complement. </li></ul>
What is the complement of 60°?  <ul><li>30° </li></ul>
What is the complement of 35°?  <ul><li>55° </li></ul>
What is the complement of 23°?  <ul><li>67° </li></ul>
What is the complement of 81°?  <ul><li>9° </li></ul>
What is the complement of 77°?  <ul><li>13° </li></ul>
What is the complement of 3°?  <ul><li>87° </li></ul>
What is the complement of 45°?  <ul><li>45° </li></ul>
<ul><li>Find the supplement. </li></ul>
What is the supplement of 30°?  <ul><li>150° </li></ul>
What is the supplement of 112°?  <ul><li>68° </li></ul>
What is the supplement of 95°?  <ul><li>85° </li></ul>
What is the supplement of 47°?  <ul><li>133° </li></ul>
What is the supplement of 8°?  <ul><li>172° </li></ul>
What is the supplement of 164°?  <ul><li>26° </li></ul>
What is the supplement of 146°?  <ul><li>34° </li></ul>
<ul><li>(mixed) </li></ul>
What is the complement of 59°?  <ul><li>31° </li></ul>
What is the supplement of 15°?  <ul><li>165° </li></ul>
What is the complement of 27°?  <ul><li>63° </li></ul>
What is the complement of 100°?  <ul><li>none </li></ul>
What is the supplement of 100°?  <ul><li>80° </li></ul>
What is the complement of the supplement of 146°?  <ul><li>56° </li></ul>
What is the complement of the complement of 10°?  <ul><li>10° </li></ul>
What is the supplement of the supplement of 113°?  <ul><li>113° </li></ul>
What is the complement of the supplement of 110°?  <ul><li>20° </li></ul>
What is the complement of the supplement of 35°?  <ul><li>none° </li></ul>
What is the supplement of the complement of 14°?  <ul><li>114° </li></ul>
What is the supplement of the complement of 88°?  <ul><li>178° </li></ul>
What is the complement of x°?  <ul><li>(90-x)° </li></ul>
What is the supplement of x°?  <ul><li>(180-x)° </li></ul>
<ul><li>If   BAC is 20° more than its complement, what is its measure? </li></ul>55°
<ul><li>An angle measures twice the measure of its complement. What is the angle? </li></ul>60°
<ul><li>Angle BUM is 30° less than twice its complement. Find its measurement. </li></ul>50°
<ul><li>An angle and its complement have a ratio of 2:3. What are their measurements? </li></ul>36°, 54°
<ul><li>The difference between the measures of angle and its complement is 36°. Find their measurements. </li></ul>63°, 27°
<ul><li>Angle CAT and angle DOG are supplementary. If m  CAT is thrice the m  DOG, what are their measurements? </li></u...
<ul><li>Find the size of the angle whose supplement is equal to six times its complement. </li></ul>72°
<ul><li>The supplement of an angle measures 40° more than twice its complement. What is the measurement of the angle?  </l...
<ul><li>The difference between the measures of two supplementary angles is 50 0 . Find the measure of the larger angle.  <...
 
Find the measure of   R if: <ul><li>it is 50° more than its complement. </li></ul><ul><li>it is 12° less than its complem...
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Angles

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Transcript of "Angles"

  1. 5. ANGLES
  2. 6. <ul><li>An angle ( ) is formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle). </li></ul><ul><li>PARTS OF AN ANGLE </li></ul><ul><li>Vertex: A </li></ul><ul><li>B Sides: AB and AC </li></ul><ul><li>exterior of the angle </li></ul><ul><li>interior of </li></ul><ul><li>the angle </li></ul><ul><li>A 1 C </li></ul><ul><li>HOW TO NAME AN ANGLE </li></ul><ul><ul><li>- BAC - CA B - 1 - A </li></ul></ul><ul><li>Angles are measured in degrees. </li></ul><ul><li>The measure of A is written as m A. m A = 45 o . </li></ul>
  3. 7. CLASSIFICATION OF ANGLES (according to measure) <ul><li>x o </li></ul><ul><li>ACUTE x o x o </li></ul><ul><li>0 < x < 90 o RIGHT </li></ul><ul><li>x = 90 o </li></ul><ul><li>REFLEX </li></ul><ul><li>x o 180 o < x < 360 o x o </li></ul><ul><li>OBTUSE STRAIGHT </li></ul><ul><li>90 o < x < 180 o x = 180 o </li></ul>
  4. 8. PROTRACTOR POSTULATE <ul><li>Let OA and OB be opposite rays in a plane. OA, OB and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers from 0 o to 180 o in such a way that OA is paired with 0 o to and OB is paired with 180 o or the way around. </li></ul><ul><ul><li>Angles with the same measure are congruent. </li></ul></ul>
  5. 9. ANGLE ADDITION POSTULATE <ul><li>If point B is in the interior of  AOC, then </li></ul><ul><li>m  AOB + m  BOC = m  AOC . </li></ul><ul><li>If  AOC is a straight angle, then </li></ul><ul><li> m  AOB + m  BOC = 180 o . </li></ul>
  6. 10. Angle Pairs <ul><li>Two coplanar angles are adjacent if and only if they satisfy three conditions: </li></ul><ul><ul><li>they have a common vertex, </li></ul></ul><ul><ul><li>they have common side, and </li></ul></ul><ul><ul><li>they have no common interior points. </li></ul></ul><ul><ul><li> AOB and  BOC are adjacent. </li></ul></ul><ul><ul><li> ABC and  DEF are not. </li></ul></ul>
  7. 11. <ul><li>Two angles are complementary if and only if the sum of their measures is equal to 90 o . Each angle is the complement of the other. </li></ul><ul><li>Two angles are supplementary if and only if the sum of their measures is equal to 180 o . Each angle is the supplement of the other </li></ul>
  8. 12. <ul><li>Find the complement. </li></ul>
  9. 13. What is the complement of 60°? <ul><li>30° </li></ul>
  10. 14. What is the complement of 35°? <ul><li>55° </li></ul>
  11. 15. What is the complement of 23°? <ul><li>67° </li></ul>
  12. 16. What is the complement of 81°? <ul><li>9° </li></ul>
  13. 17. What is the complement of 77°? <ul><li>13° </li></ul>
  14. 18. What is the complement of 3°? <ul><li>87° </li></ul>
  15. 19. What is the complement of 45°? <ul><li>45° </li></ul>
  16. 20. <ul><li>Find the supplement. </li></ul>
  17. 21. What is the supplement of 30°? <ul><li>150° </li></ul>
  18. 22. What is the supplement of 112°? <ul><li>68° </li></ul>
  19. 23. What is the supplement of 95°? <ul><li>85° </li></ul>
  20. 24. What is the supplement of 47°? <ul><li>133° </li></ul>
  21. 25. What is the supplement of 8°? <ul><li>172° </li></ul>
  22. 26. What is the supplement of 164°? <ul><li>26° </li></ul>
  23. 27. What is the supplement of 146°? <ul><li>34° </li></ul>
  24. 28. <ul><li>(mixed) </li></ul>
  25. 29. What is the complement of 59°? <ul><li>31° </li></ul>
  26. 30. What is the supplement of 15°? <ul><li>165° </li></ul>
  27. 31. What is the complement of 27°? <ul><li>63° </li></ul>
  28. 32. What is the complement of 100°? <ul><li>none </li></ul>
  29. 33. What is the supplement of 100°? <ul><li>80° </li></ul>
  30. 34. What is the complement of the supplement of 146°? <ul><li>56° </li></ul>
  31. 35. What is the complement of the complement of 10°? <ul><li>10° </li></ul>
  32. 36. What is the supplement of the supplement of 113°? <ul><li>113° </li></ul>
  33. 37. What is the complement of the supplement of 110°? <ul><li>20° </li></ul>
  34. 38. What is the complement of the supplement of 35°? <ul><li>none° </li></ul>
  35. 39. What is the supplement of the complement of 14°? <ul><li>114° </li></ul>
  36. 40. What is the supplement of the complement of 88°? <ul><li>178° </li></ul>
  37. 41. What is the complement of x°? <ul><li>(90-x)° </li></ul>
  38. 42. What is the supplement of x°? <ul><li>(180-x)° </li></ul>
  39. 43. <ul><li>If  BAC is 20° more than its complement, what is its measure? </li></ul>55°
  40. 44. <ul><li>An angle measures twice the measure of its complement. What is the angle? </li></ul>60°
  41. 45. <ul><li>Angle BUM is 30° less than twice its complement. Find its measurement. </li></ul>50°
  42. 46. <ul><li>An angle and its complement have a ratio of 2:3. What are their measurements? </li></ul>36°, 54°
  43. 47. <ul><li>The difference between the measures of angle and its complement is 36°. Find their measurements. </li></ul>63°, 27°
  44. 48. <ul><li>Angle CAT and angle DOG are supplementary. If m  CAT is thrice the m  DOG, what are their measurements? </li></ul>135°, 45°
  45. 49. <ul><li>Find the size of the angle whose supplement is equal to six times its complement. </li></ul>72°
  46. 50. <ul><li>The supplement of an angle measures 40° more than twice its complement. What is the measurement of the angle? </li></ul>40°
  47. 51. <ul><li>The difference between the measures of two supplementary angles is 50 0 . Find the measure of the larger angle. </li></ul>115°
  48. 53. Find the measure of  R if: <ul><li>it is 50° more than its complement. </li></ul><ul><li>it is 12° less than its complement. </li></ul><ul><li>it is thrice its complement. </li></ul><ul><li>it is half its complement. </li></ul><ul><li>it is 58° more than thrice its complement. </li></ul><ul><li>it is twice the measure of its supplement. </li></ul><ul><li>it is 44° less than its supplement. </li></ul><ul><li>its supplement is thrice its complement. </li></ul><ul><li>its complement and supplement add up to 120 ° . </li></ul><ul><li>its complement is 90° less than its supplement. </li></ul>
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