My fraction (not necessarily in simplest form) can be simplified to $\dfrac{5}{9}.$ When $5$ is added to the denominator of this fraction, the resulting fraction can be simplified to $\dfrac{1}{2}.$ What is the sum of the numerator and denominator of my fraction?

Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem