Solve for X in Intersecting Lines: Finding Angles 2X-9 and 5+X

Let us solve this step-by-step:

• Step 1: Identify the angle relationship.
  Since the angles are positioned on opposite sides of the transversal and between the two parallel lines, we can posit that these angles are alternate interior angles. These angles are equal when the lines are parallel.

• Step 2: Set up the equation.
  Since the alternate interior angles are equal, we set the expressions equal to one another:
  $2X - 9 = 5 + X$

• Step 3: Solve the equation for $X$.
  Subtract $X$ from both sides to get: $2X - X - 9 = 5$ which simplifies to: $X - 9 = 5$ Add $9$ to both sides to find: $X = 14$

The value of $X$ calculated is consistent with the nature of the angle relationships in parallel lines cut by a transversal.

Therefore, the solution to the problem is $X = 14$.