Geometry problem me out

m> 1=(45 x-30)° , m< 5=(20 x+70)°

  see below

Step-by-step explanation:

Angles 1 and 5 are both outside (not between) the parallel lines, so are "exterior" angles. Angle 1 is on the northwest corner of the intersection; angle 5 is on the southeast corner, so they are not "corresponding." Rather, they are "alternate".

The only answer choice properly describing the angles also properly shows their measure:

  Alt Ext ∠s Thm

  ∠1 ≅ ∠5 = 150°

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Since the angles are equal, you can write the equation ...

  45x -30 = 20x +70

  25x = 100 . . . . . . . . . add 30-20x

  x = 4 . . . . . . . . . . . . . divide by 25

We can substitute this value into the expression for angle 5:

  20x +70 = 20·4 +70 = 150 . . . . . the angle measures are 150°