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DochEvi [55]
4 years ago
5

If L is parallel to M, find the value of each variable(s)

Mathematics
1 answer:
Anna71 [15]4 years ago
6 0

Answer:

see below

Step-by-step explanation:

5.  9x + 2 = 119°                    alternate interior angles are congruent

          9x = 117

           x = 13°

6.  12x - 8 + 104° = 180°       same side interior angles are supplementary

            12x + 96 = 180

                     12x = 84

                        x = 7°

7.  5x + 7 = 8x - 71                alternate exterior angles are congruent

         -3x = -78

            x = 26°

8.  4x - 7 = 7x - 61                corresponding angles are congruent

        -3x = -54

          x = 18°

9.  9x + 25 = 13x - 19          corresponding angles are congruent

            -4x = -44

               x = 11°

    13x - 19 + 17y + 5 = 180°        straight line adds up to 180°

    13(11) - 19 + 17y + 5 = 180

       143 - 19 + 17y + 5 = 180

                    17y + 129 = 180

                              17y = 51

                                  y = 3°

10.  6x - 7 + 3x - 29 = 180°     same side interior angles are supplementary

                   9x - 36 = 180

                           9x = 216

                             x = 24°

     6x - 7 = 8y + 17                   vertical angles are congruent

      6(24) - 7 = 8y + 17

         144 - 7 = 8y + 17

               137 = 8y + 17

               120 = 8y

                  y = 15°

11.  49 + 3x = 7x - 23                corresponding angles are congruent

            -4x = -72

               x = 18°

 

      3x = 11y - 1                         corresponding angles are congruent

      3(18) = 11y - 1      

          54 = 11y - 1

          55 = 11y

            y = 5°

12.  5x - 38 = 3x - 4                alternate interior angles are congruent

             2x = 34

               x = 17°

 

      7y - 20 + 5x - 38 + 90 = 180°        sum of triangle interior angle equals 180

      7y - 20 + 5(17) - 38 + 90 = 180°      

      7y - 20 + 85 - 38 + 90 = 180°    

                              7y + 117 = 180

                                      7y = 63

                                       y = 9°

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