Question

please answer this question

Answer 1

Answer:

       Fig 1

if it is given 4x, then the angle opposite will be 4x, too.

       4x = angle 2 = 4x ( vertically opposite angles )

       angle 2 and x form interior angles on the same side of the transversal.

       4x+x = 180 degrees

        5x = 180

        x = 36 degrees

       Fig 2              

      55 degrees = angle 2 ( vertically opposite angles )

       angle 1 = 68 degrees ( corresponding angles )

        angle 1 + angle 2 + angle 3 = 180 degrees ( sum of all angles of a triangle is 180)

         68 + 55 + angle 3 = 180

         123 + angle 3 = 180

         angle 3 = 180 - 123

         angle 3 = 57 degrees

       

         angle 3 = angle 4 ( corresponding angles )

         57 = angle 4

         angle 4 and x make a linear pair.

         57 + x = 180 ( linear pair )

         x = 180 - 57

         x = 123 degrees

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Answer 2

Answer:

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