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Vertical , Complementary, and Supplementary Angles

Unit 1 Part 5. Vertical , Complementary, and Supplementary Angles. Vertical angles are congruent. C. B. A. D. ∠ A is congruent to ∠ B. Opposite angles. ∠ C is congruent to ∠ D. Complementary angles. Two adjacent angles whose sum equals 90 degrees. A B. C. D.

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Vertical , Complementary, and Supplementary Angles

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  1. Unit 1 Part 5 • Vertical , Complementary, and Supplementary Angles

  2. Vertical angles are congruent. C B A D ∠ A is congruent to ∠ B Opposite angles ∠ C is congruent to ∠ D

  3. Complementary angles • Two adjacent angles whose sum equals 90 degrees. A B C D ∠ACB + ∠ BCD = 90 degrees

  4. Complementary angles

  5. Supplementary angles • Two adjacent angles whose sum equals 180 degrees. G K L M ∠ KLG + ∠ GLM = 180 degrees

  6. Supplementary angles

  7. Problems • If angle A is x + 10 and angle B is 4x – 35 then what is the value of x and the measure of angle A ? C B A D

  8. Solution • X + 10 = 4x – 35 • - 10 - 10 • x = 4x – 45 • -4x -4x • -3x = -45 • -3 -3 • x = 15 , m ∠ A = 25 C B A D

  9. Problems • Angle ABD and angle DBC are complementary angles (equals 90 degrees). If m∠ ABD = (3x – 1)° and m∠ DBC = (2x + 6)° what is the measure of m∠ ABD. A D B C

  10. Solution • ∠ ABD + ∠ DBC = 90 • 2x + 6 + 3x – 1 = 90 • 5x + 5 = 90 (gather) • -5 -5 (separate) • 5x = 85 • X= 17 • 2(17) + 6 = 40 degrees  m ∠ ABD A D B C

  11. Problems • ∠ A and ∠ B are supplementary angles. ( equals 180 degrees) If m∠A = 75 degrees how much is angle B ? • m∠A + m∠B = 180 • 75 + ∠B = 180 • -75 -75 • m∠B = 105 degrees

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