1. **State the problem:** We are given a trapezium with two angles on the left side: the top-left angle is $97 - 3x$ degrees and the bottom-left angle is $69 + 5x$ degrees. We need to find the value of $x$. 2. **Important rule:** In a trapezium, the consecutive angles between the parallel sides are supplementary, meaning they add up to $180^\circ$. 3. **Apply the rule:** Since the left side is vertical and the top and bottom sides are parallel, the top-left and bottom-left angles are consecutive angles between the parallel sides. Therefore, $$ (97 - 3x) + (69 + 5x) = 180 $$ 4. **Simplify the equation:** $$ 97 - 3x + 69 + 5x = 180 $$ $$ (97 + 69) + (-3x + 5x) = 180 $$ $$ 166 + 2x = 180 $$ 5. **Solve for $x$:** $$ 2x = 180 - 166 $$ $$ 2x = 14 $$ $$ x = \frac{14}{2} = 7 $$ 6. **Final answer:** $$ \boxed{7} $$ Thus, the value of $x$ is 7.