First, recognize that when added, the two angles in question will equal 180 degrees. Given this information, you can set up an equation!
(12x-23) + (71-x) = 180
Using the equation, solve for x.
Combine like terms:
11x + 48 = 180
Subtract 48 from both sides:
11x = 132
Divide both sides by 11 to solve for x:
x = 12