Hint: omars equation doesn't work!
identify his error and correct it by showing the steps omar should have taken and determine the correct value of x.

His Error: He set the expressions 10x-1 and 59 equal to each other. Those two angles are not congruent. 

He should have added the two expressions to get 180
(10x-1) + (59) = 180
10x+(-1+59) = 180
10x+58 = 180
10x+58-58 = 180-58
10x = 122
10x/10 = 122/10
x = 12.2

20x < 100

subtract 20 from both sides

20 - 20 = 0

100 - 20 = 80

x < 80