1. **Problem Statement:** Given two parallel lines AB and JK, and a transversal intersecting them, find the value of $x$ given the angles $y^\circ$, $(5x - 21)^\circ$, and $(2x - 9)^\circ$. 2. **Relevant Geometry Rule:** When two parallel lines are cut by a transversal, alternate interior angles are equal, and corresponding angles are equal. 3. **Identify Angles:** From the diagram description, the angles $(5x - 21)^\circ$ and $(2x - 9)^\circ$ are likely alternate interior angles or corresponding angles, so they are equal. 4. **Set up the equation:** $$ 5x - 21 = 2x - 9 $$ 5. **Solve for $x$:** $$ 5x - 21 = 2x - 9 \\ 5x - 2x = -9 + 21 \\ 3x = 12 \\ x = \frac{12}{3} $$ 6. **Cancel common factors:** $$ x = \cancel{\frac{12}{3}} = 4 $$ 7. **Final answer:** $$ x = 4 $$ This means the value of $x$ that satisfies the angle relationships given the parallel lines and transversal is 4.