1. **State the problem:** We are given a quadrilateral with angles 113°, 98°, 42°, and an unknown angle $x$. We need to find the value of $x$. 2. **Formula used:** The sum of the interior angles of any quadrilateral is always 360°. This is given by: $$113^\circ + 98^\circ + 42^\circ + x = 360^\circ$$ 3. **Calculate the sum of the known angles:** $$113 + 98 + 42 = 253$$ 4. **Set up the equation to solve for $x$:** $$253 + x = 360$$ 5. **Isolate $x$ by subtracting 253 from both sides:** $$\cancel{253} + x = 360 - \cancel{253}$$ $$x = 107$$ 6. **Answer:** The value of $x$ is $107^\circ$. This means the unknown angle in the quadrilateral is 107 degrees.