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Warm Up Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)

Warm Up Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10) Write an algebraic expression for each of the following. 3. 4 more than twice a number 4. 6 less than half a number. 70 – x. 190 – 3 x. 2 n + 4. 11. 1 or JMK; 2 or LMK; M or JML

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Warm Up Simplify each expression. 1. 90 – ( x + 20) 2. 180 – (3 x – 10)

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  1. Warm Up Simplify each expression. 1.90 –(x + 20) 2. 180 – (3x – 10) Write an algebraic expression for each of the following. 3. 4 more than twice a number 4. 6 less than half a number 70 –x 190 –3x 2n + 4

  2. 11. 1 or JMK; 2 or LMK; M or JML • 12. 90°; rt 35. mCOD = mBOC = 9° • 13. 93°; obtuse 36. ROCK = 90°; R & B = 108°; • 14. 20°; acute JAZZ = 126°; RAP = 36° • 66.6° 41. D • 36.8° 42. H • 17. 20° 43. C • 18. 25° 44. J • 27. 67.5°; 22.5° 53 - 55. see drawings • 29. 16 1/3 56. 2 • 30. 10 57. 6 • 31. 9 58. 8 • 32. 72° • 34. mAOB = 90°; RT mBOC = 126°; OBTUSE • mCOD = 36°; ACUTE mDOA = 108°; OBTUSE

  3. Example 1 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. adjacent, linear line A. 5 and 6 adjacent B. 7 and SPU not adjacent C. 7 and 8

  4. You can find the complement of an angle that measures x° by subtracting its measure from 90°, or (90 – x)°. You can find the supplement of an angle that measures x° by subtracting its measure from 180°, or (180 – x)°.

  5. Example 2 Find the measure of each of the following. a. complement of E (90– x)° 90°–(7x – 12)°=90°– 7x°+ 12° = (102 – 7x)° b. supplement of F (180– x) 180 – 116.5°=

  6. Example 3A An angle is 10° more than 3 times the measure of its complement. Find the measure of the complement. Step 1 Let mA = x°. Then B, its complement measures (90 – x)°. Step 2 Write and solve an equation. x = 3(90 – x) + 10 x = 270 – 3x + 10 x = 280 – 3x 4x = 280 x = 70 The measure of the complement, B, is (90 – 70) = 20.

  7. Example 3B An angle’s measure is 12° more than the measure of its supplement. Find the measure of the angle. x = 0.5(180 – x) + 12 x = 90 – 0.5x + 12 x = 102 – 0.5x 1.5x = 102 x = 68 The measure of the angle is 68.

  8. Example 4 Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary. If m1 = 47°, find m2, m3, and m4. Think of the important information: • 1 2 • 1 and 3 are complementary, and 2 and 4 are complementary. • m1 = 47° m 1 = m 2 = 47° If 3 and 1 are complementary, then m3 = (90 – 47)° = 43°. If 4 and 1 are complementary, then m4 = (90 – 47)° = 43°.

  9. Vertical angles: two nonadjacent angles formed by two intersecting lines. 1and 3are vertical angles, as are 2and 4. Example 5 Name the pairs of vertical angles. HML and JMK are vertical angles. HMJ and LMK are vertical angles. pg. 32 ________________________________________________________

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