In the figure below

Explanation

1. Because the angles are interior angles on the same side of the transversal, they are supplementary.
   The sum of the measures of two supplementary
   • The sum of the measures of two supplementary angles is 180^o
     • 3x - 80^o + 3x + 20^o = 180^o
   • Combine like terms: 3x + 3x = 6x
     • 6x - 60^o = 180^o
   • To undo the subtraction of 60^o, add 60^o to both sides: 180^o + 60^o = 240^o
     • 6x = 240^o
   • To isolate x, undo the multiplication by 6 by dividing both sides by 6
     • x = 40^o
   • Thus, x is 40^o
2. To find the measures of the angles in the figure, we evaluate the expressions 3x + 20^o and 3x - 80^o for x = 40^o
   1. 3x + 20^o = 3(40^o) + 20^o = 120^o + 20^o = 140^o
   2. 3x - 80^o = 3(40^o) - 80^o = 120^o - 80^o = 40^o