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Understanding Supplementary, Complementary, and Opposite Angles

This document explores the concepts of supplementary, complementary, and opposite angles through mathematical definitions and examples. Supplementary angles sum to 180 degrees, while complementary angles sum to 90 degrees. The text illustrates how to determine the measures of these angles and identifies their relationships through corresponding, alternate interior, and consecutive angles. Practical examples, including algebraic expressions for angles, help clarify the calculations and reinforce learning.

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Understanding Supplementary, Complementary, and Opposite Angles

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  1. ANGLE AND LINE By: NIKMATUL HUSNA

  2. SUPPLEMENTARY AOC +  BOC =  AOB a0 + b0 = 1800 We can write a0 = 1800 - b0 or b0 = 1800 - a0

  3. Conclusion : • The sum of supplementary angle is 1800. • An angle is the supplement of another angle

  4. COMPLEMENTARY PQS +  RQS =  PQR X0 + Y0 = 900 We can write X0 = 900 - Y0 or Y0 = 900 - X0

  5. Conclusion : • The sum of complementary angle is 900. • An angle is the complement of another angle

  6. OPPOSITE ANGLE • POQ =  SOR • POS =  QOR • POQ and  SOR are opposite angle. • POS and  QOR are opposite angle.

  7. Conclusion : • The measure of opposite angle is same

  8. Opposite Angles 1and 7 2and 8 3and 5 4and 6 5 6 4 7 8 3 2 t 1 1 = 7, 2= 8, 3= 5, 4= 6

  9. 5 6 4 7 8 3 2 t 1 • Corresponding Angles • Alternate Interior Angles • Alternate Exterior Angles • Consecutive Interior Angles • Consecutive Exterior Angles

  10. Corresponding Angles 4 and 2 3 and 1 5 and 7 6 and 8 5 6 4 7 8 3 2 t 1 4 = 2, 3 = 1, 5 = 7, 6 = 8

  11. Alternate Interior Angles 3 and 7 2 and 6 5 6 4 7 8 3 2 t 1 3 = 7 and2 = 6

  12. Alternate Exterior Angles 5 and 1 4 and 8 5 6 4 7 8 3 2 t 1 5 = 1 and4 = 8

  13. Consecutive Interior Angles 5 3 and 2 6 and 7 6 4 7 8 3 2 t 1 3 +2 = 1800 and 6 +7 = 1800

  14. Consecutive Exterior Angles 5 4 and 1 5 and 8 6 4 7 8 3 2 t 1 4 + 1 = 1800 and 5 + 8 = 1800

  15. 5 6 4 7 8 3 2 t 1 Example : Look at the picture. Given 1 = 750 and Find: • 1 5 • 2 6 • 3 7 • 4 8

  16. Answer : • 1 = 7505 = 750 • 2 =1050 6 = 1050 • 3=750 7= 750 • 4=1050 8= 1050

  17. 5 6 4 7 8 3 2 t 1 Example : Look at the picture. Given 1 = (3x+45)0 and 4 =(5x+23)0 . Find: • 1 5 • 2 6 • 3 7 • 4 8

  18. Answer : • 1 +4 =1800 (3x+45)0 + (5x+23)0 =1800 3x0+ 5x 0 +45 0 + 23 0 =1800 8x0 =1800- 450 – 230 8x0 =112 0 x = 140

  19. 1=(3x+45)0= 3 X 140 +450 = 420 +450 = 870  4=1800- 870 = 930  2= 930  3= 870  5= 870  6= 930  7= 870  8= 930

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