1. **State the problem:** We need to find the size of the exterior angle $x$ in a quadrilateral where the interior angles given are $90^\circ$, $80^\circ$, $65^\circ$, and one unknown exterior angle $x$ adjacent to the $65^\circ$ interior angle. 2. **Recall the rule for exterior angles:** An exterior angle and its adjacent interior angle are supplementary, meaning their sum is $180^\circ$. 3. **Apply the rule:** Since $x$ is exterior to the $65^\circ$ interior angle, we have $$x + 65^\circ = 180^\circ$$ 4. **Solve for $x$:** $$x = 180^\circ - 65^\circ$$ $$x = 115^\circ$$ 5. **Verify the quadrilateral angle sum:** The sum of interior angles in any quadrilateral is $360^\circ$. The given interior angles are $90^\circ$, $80^\circ$, $65^\circ$, and the fourth angle adjacent to $x$ is not directly given but can be found by subtracting the exterior angle from $180^\circ$ if needed. **Final answer:** $$\boxed{115^\circ}$$