1. **State the problem:** We need to find the range of possible values of $x$ given a quadrilateral with one internal angle labeled as $(3x - 6)^\circ$, an adjacent angle of $24^\circ$, and two side lengths $36$ and $34$ units. 2. **Recall the rule for quadrilateral angles:** The sum of the internal angles of any quadrilateral is $360^\circ$. 3. **Set up the equation:** Let the other two angles be $A$ and $B$. Then, $$ (3x - 6) + 24 + A + B = 360 $$ 4. **Analyze the problem:** Since the problem only gives two angles and two side lengths, and asks for the range of $x$ based on the angle $(3x - 6)^\circ$, we consider the constraints on angles in a quadrilateral: - Each angle must be greater than $0^\circ$ and less than $180^\circ$ (since internal angles in a simple quadrilateral are less than $180^\circ$). 5. **Apply constraints to $(3x - 6)^\circ$:** $$ 0 < 3x - 6 < 180 $$ 6. **Solve inequalities:** - For the left inequality: $$ 3x - 6 > 0 $$ $$ 3x > 6 $$ $$ x > 2 $$ - For the right inequality: $$ 3x - 6 < 180 $$ $$ 3x < 186 $$ $$ x < 62 $$ 7. **Combine results:** $$ 2 < x < 62 $$ **Final answer:** The range of possible values of $x$ is $$ \boxed{2 < x < 62} $$