Angle Pairs

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Angle Pairs

  1. 1. Angle Pairs<br />
  2. 2. Complementary Angles<br />Complementary angles are two angles whose measures have a sum of 90°.<br />
  3. 3. Complementary Angles<br />These two angles (40° and 50°) are complementary because they add up to 90°. <br />But the angles don't have to be together.These two are complementary because<br />27° + 63° = 90°.<br />
  4. 4. Given that the two angles below are complementary, solve for the value of x and the angle measurements.<br />mA 30<br />mB  2x + 10<br /> 30°<br /> 60°<br />mA + mB<br />30 + 2x + 10<br />2x<br />2x<br />x<br />90<br />90<br />90 – 30 – 10<br />50<br />25<br />=<br />=<br />=<br />=<br />=<br />
  5. 5. Given that the two angles below are complementary, solve for the value of x and the angle measurements.<br />mC 2x + 20<br />mD  3x – 5<br /> 50°<br /> 40°<br />mC + mD<br />2x + 20 + 3x – 5<br />2x + 3x<br />5x<br />x<br />90<br />90<br />90 – 20 + 5<br />75<br />15<br />=<br />=<br />=<br />=<br />=<br />
  6. 6. Given that the two angles below are complementary, solve for the value of x and the angle measurements.<br />mFEG 35 – x<br />mGEH  45 + 2x<br /> 25°<br /> 65°<br />mFEG + mGEH<br />35 – x + 45 + 2x<br />– x + 2x<br />x<br />90<br />90<br />90 – 35 – 45<br />10<br />=<br />=<br />=<br />=<br />
  7. 7. Solve for the value of x and the measurements of the angles, given that each pair of angles are complementary.<br />J = (5x – 18)° & K = (4x)°<br />L = (45 – 2x)° & M = (40 + 3x)°<br />NOP = (5x – 20) & POQ = (x – 10)°<br />1 = (45 – x)° & 2 = (2x + 15)°<br />R = x° & S = (2x + 6) °<br />
  8. 8. Solve for the value of x and the measurements of the angles, given that each pair of angles are complementary.<br />J = (5x – 18)° & K = (4x)° 12 42 48<br />L = (45 – 2x)° & M = (40 + 3x)° 5 35 55<br />NOP = (5x – 20) & POQ = (x – 10)° 20 80 10<br />1 = (45 – x)° & 2 = (2x + 15)° 30 15 75<br />R = x° & S = (2x + 6) ° 28 28 62<br />
  9. 9. Supplementary Angles<br />Supplementary angles are two angles whose measures have a sum of 180°.<br />
  10. 10. Supplementary Angles<br />These two angles (140° and 40°) are supplementary because they add up to 180°. <br />But the angles don't have to be together.These two are supplementary because<br />27° + 63° = 180°.<br />
  11. 11. Given that the two angles below are supplementary, solve for the value of x and the angle measurements.<br />mT 50<br />mV  3x + 40<br /> 50°<br /> 130°<br />mT + mV<br />50 + 3x + 40<br />3x<br />3x<br />X<br />180<br />180<br />180 – 50 – 40<br />90<br />30<br />=<br />=<br />=<br />=<br />=<br />
  12. 12. Given that the two angles below are supplementary, solve for the value of x and the angle measurements.<br />mW 3x – 55<br />mX  155 – x<br /> 65°<br /> 115°<br />mW + mX<br />3x – 55 + 155 – x<br />3x – x<br />2x<br />x<br />180<br />180<br />180 + 55 – 155<br />80<br />40<br />=<br />=<br />=<br />=<br />=<br />
  13. 13. Given that the two angles below are supplementary, solve for the value of x and the angle measurements.<br />mBYA 3x + 5<br />mAYZ  2x<br /> 110°<br /> 70°<br />mBYA + mAYZ<br />3x + 5 + 2x<br />3x + 2x<br />5x<br />x<br />180<br />180<br />180 – 5<br />175<br />35<br />=<br />=<br />=<br />=<br />=<br />
  14. 14. Solve for the value of x and the measurements of the angles, given that each pair of angles are supplementary.<br />C = (2x – 2)° & D = (x – 34)°<br />3 = (3x + 5)° & 4 = (5x + 5)°<br />EFG = (x – 20)° & GFH = (x + 60)°<br />J = (150 – x)° & K = (2x – 70)°<br />LMN = (2x + 1)° & PQR = (3x – 1)°<br />
  15. 15. Solve for the value of x and the measurements of the angles, given that each pair of angles are supplementary.<br />C = (2x – 2)° & D = (x – 34)° 72 142 38<br />3 = (3x + 5)° & 4 = (5x + 5)° 15 100 80<br />EFG = (x – 20)° & GFH = (x + 60)° 80 60 120<br />J = (150 – x)° & K = (2x – 70)° 100 50 130<br />LMN = (2x + 1)° & PQR = (3x – 1)° 36 73 107<br />
  16. 16. The Complement Theorem: Complements of congruent angles are congruent.<br /> Given:<br />C and O are complementary<br /> P and M are complementary<br /> O  M<br /> Prove:<br /> C  P<br />
  17. 17. The Complement Theorem: Complements of congruent angles are congruent.<br />STATEMENT<br />C and O are complementary<br />P and M are complementary<br />O  M<br />mC + mO = 90<br />mP + mM = 90<br />mC + mO = mP + mM<br />mO = mM<br />mC = mP<br />C  P<br />REASON<br />Given<br />Definition of complementary angles<br />Transitive Property of Equality<br />Definition of congruent angles<br />Subtraction Property of Equality<br />Definition of congruent angles<br />
  18. 18. Theorem: If two angles are complementary and adjacent, then they form a right angle.<br />
  19. 19. The Supplement Theorem: Supplements of congruent angles are congruent.<br />
  20. 20. Linear Pair<br />A linear pair consists of two adjacent angles whose noncommon sides are opposite rays.<br />Linear Pair Postulate: If two angles form a linear pair, then they are supplementary.<br />
  21. 21. Vertical Angles<br />Vertical angles are two nonadjacent angles formed by two intersecting lines.<br />
  22. 22. Vertical Angle Theorem: Vertical angles are congruent.<br />

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