Step-by-step explanation:Since, lines l and m are parallel and a transverse is intersecting these lines.5). (9x + 2)° = 119° [Alternate intrior angles]9x = 117 ⇒ x = 136). (12x - 8)° + 104° = 180°12x = 180 - 96x =  ⇒ x = 77). (5x + 7) = (8x - 71) [Alternate exterior angles]8x - 5x = 71 + 73x = 78x = 268). (4x - 7) = (7x - 61) [Corresponding angles]7x - 4x = -7 + 613x = 54x = 189). (9x + 25) = (13x - 19) [Corresponding angles]13x - 9x = 25 + 194x = 44(13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary](13×11) - 19 + 17y + 5 = 180129 + 17y = 18017y = 180 - 129y = 310). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]3x + 8y = 180 + 123x + 8y = 192 -----(1)(8y + 17) = (6x - 7) [Alternate exterior angles]6x - 8y = 243x - 4y = 12 -----(2)Equation (1) - equation (2)(3x + 8y) - (3x - 4y) = 192 - 1212y = 180y = 15From equation (1),3x + 8(15) = 1923x + 120 = 192x = 2411). (3x + 49)° = (7x - 23)° [Corresponding angles]7x - 3x = 49 + 234x = 72 ⇒ x = 18(11y - 1)° = (3x)° [Corresponding angles]11y = 3×18 + 111y = 55 ⇒ y = 512). (5x - 38)° = (3x - 4)° [Corresponding angles]5x - 3x = 38 - 42x = 34x = 17(7y - 20)° + (5x - 38)° + 90° = 180°[Sum of interior angles of a triangle = 180°]5x + 7y = 1485×17 + 7y = 14885 + 7y = 1487y = 148 - 85y =...

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