For questions 18-20, if l \\ m, find the values of x and y

Step-by-step explanation:

18). l║m and a transverse is intersecting these lines.

     (11y - 32)° = (6x + 7)° [Vertical angles]

     -6x + 11y = 39 -------(1)

      (3x - 16)° + (6x + 7)°= 180°  [Same side exterior angles]

      9x - 9 = 180

      9x = 189

      x = 21

      Now substitute the value of x in the equation (1)

      -6(21) + 11y = 39

      11y = 39 + 126

      y = 15

19). l║m and a transversal is intersecting these lines.

     (8x - 14)° + (5y + 16)° = 180° [Linear pair of angles]

      8x + 5y = 178 --------(1)

      (8x - 14)° = (5x + 34)° [Alternate exterior angles]

      8x - 5x = 48

      3x = 48

      x = 16

      From equation (1)  

      8(16) + 5y = 178

      128 + 5y = 178

      5y = 178 - 128

      y = 10

20). From the figure attached,

      m∠CAB = (5y - 23)°

      Since sum of interior angles of a triangle is 180°

     m∠CAB + m∠ACB + m∠ABC = 180°

      (5y - 23)° + (2x + 13)° + (47)° = 180°

      2x + 5y = 143 ------(1)

      (5y - 23)° = 3x°

      3x - 5y = -23 -----(2)

      Equation (1) + Equation (2)

      (2x + 5y) + (3x - 5y) = 143 - 23

      5x = 120

      x = 24

      From equation (1)

      2(24) + 5y = 143    

      48 + 5y = 143

      5y = 95

      y = 19          

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step-by-step explanation:

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