1. **State the problem:** We are given a pentagon with interior angles labeled as 125°, (x + 7)°, 107°, (x - 15)°, and 131°. We need to find the value of $x$. 2. **Recall the formula for the sum of interior angles of a polygon:** For a polygon with $n$ sides, the sum of interior angles is given by: $$\text{Sum} = (n - 2) \times 180^\circ$$ Since this is a pentagon, $n = 5$, so: $$\text{Sum} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$$ 3. **Set up the equation:** The sum of all interior angles equals 540°, so: $$125 + (x + 7) + 107 + (x - 15) + 131 = 540$$ 4. **Simplify the equation:** Combine like terms: $$125 + 7 + 107 - 15 + 131 + x + x = 540$$ Calculate the constants: $$ (125 + 7 + 107 - 15 + 131) + 2x = 540$$ $$ (355) + 2x = 540$$ 5. **Isolate $x$:** $$2x = 540 - 355$$ $$2x = 185$$ 6. **Solve for $x$:** $$x = \frac{185}{2}$$ Show cancellation: $$x = \frac{\cancel{185}}{\cancel{2}}$$ $$x = 92.5$$ **Final answer:** $$x = 92.5^\circ$$