1. **State the problem:** We need to find the size of angle $x$ in an irregular quadrilateral where the other three angles are $57^\circ$, $32^\circ$, and $102^\circ$, and there is an interior angle marked $253^\circ$. 2. **Recall the formula:** The sum of the interior angles of any quadrilateral is always $360^\circ$. 3. **Important rule:** The sum of all interior angles in a quadrilateral is given by: $$57^\circ + 32^\circ + 102^\circ + x = 360^\circ$$ 4. **Calculate the sum of the known angles:** $$57 + 32 + 102 = 191$$ 5. **Set up the equation to find $x$:** $$191 + x = 360$$ 6. **Solve for $x$:** $$x = 360 - 191 = 169$$ 7. **Interpret the 253° angle:** The $253^\circ$ angle inside the quadrilateral is likely an exterior reflex angle and does not affect the sum of the interior angles. **Final answer:** $$\boxed{169^\circ}$$