Question

Unit 3 parallel and perpendicular lines Homework 3 proving lines are parallel

Answer 1

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 = 13

6). (12x - 8)° + 104° = 180°

 12x = 180 - 96

  x =  ⇒ x = 7

7). (5x + 7) = (8x - 71) [Alternate exterior angles]

8x - 5x = 71 + 7

3x = 78

 x = 26

8). (4x - 7) = (7x - 61) [Corresponding angles]

  7x - 4x = -7 + 61

  3x = 54

  x = 18

9). (9x + 25) = (13x - 19) [Corresponding angles]

13x - 9x = 25 + 19

  4x = 44

 

   (13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary]

   (13×11) - 19 + 17y + 5 = 180

  129 + 17y = 180

  17y = 180 - 129

  y = 3

 10). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]

  3x + 8y = 180 + 12

  3x + 8y = 192 -----(1)

(8y + 17) = (6x - 7) [Alternate exterior angles]

  6x - 8y = 24

3x - 4y = 12 -----(2)

 Equation (1) - equation (2)

(3x + 8y) - (3x - 4y) = 192 - 12

12y = 180

y = 15

 From equation (1),

 3x + 8(15) = 192

  3x + 120 = 192

x = 24

11). (3x + 49)° = (7x - 23)° [Corresponding angles]

   7x - 3x = 49 + 23

 4x = 72 ⇒ x = 18

(11y - 1)° = (3x)° [Corresponding angles]

   11y = 3×18 + 1

 11y = 55 ⇒ y = 5  

 12). (5x - 38)° = (3x - 4)° [Corresponding angles]

  5x - 3x = 38 - 4

   2x = 34

  x = 17

 (7y - 20)° + (5x - 38)° + 90° = 180°

[Sum of interior angles of a triangle = 180°]

   5x + 7y = 148

 5×17 + 7y = 148

 85 + 7y = 148

 7y = 148 - 85

 y =