1. **State the problem:** We have a trapezium symmetric about line AB. The angles given are $ (x + 33)^\circ $ at the top-left, $ (k + 33)^\circ $ at the top-right, and $ (5x - 24)^\circ $ at the bottom-left. We need to find the values of $x$ and $y$ (assuming $y = k$ since $k$ is mentioned). 2. **Use symmetry:** Since AB is the line of symmetry, the top-left and top-right angles are equal, so: $$ x + 33 = k + 33 $$ which simplifies to $$ x = k $$ 3. **Use trapezium angle properties:** The trapezium has two pairs of adjacent angles on the same side of a leg that are supplementary (sum to 180°). Since AB is the axis of symmetry, the bottom-right angle equals the bottom-left angle reflected, so bottom-right angle is also $ (5x - 24)^\circ $. 4. **Sum of angles on one leg:** The top-left and bottom-left angles are on the same leg, so: $$ (x + 33) + (5x - 24) = 180 $$ Simplify: $$ 6x + 9 = 180 $$ $$ 6x = 171 $$ $$ x = \frac{171}{6} = 28.5 $$ 5. **Find $k$:** Since $x = k$, $$ k = 28.5 $$ 6. **Find $y$:** The problem states to find $y$, but only $k$ is given. Assuming $y = k$, then $$ y = 28.5 $$ **Final answers:** $$ x = 28.5, \quad y = 28.5 $$