1. **Problem:** Find the value of $x$ given the diagonals of an isosceles trapezoid are $2x+5$ and $x+15$. 2. **Formula and rule:** In an isosceles trapezoid, the diagonals are congruent, so we set them equal: $$2x + 5 = x + 15$$ 3. **Solve for $x$:** Subtract $x$ from both sides: $$2x - x + 5 = 15$$ Simplify: $$x + 5 = 15$$ Subtract 5 from both sides: $$x = 15 - 5$$ $$x = 10$$ 4. **Explanation:** Since the diagonals are equal in length, setting their expressions equal allows us to find the value of $x$ that satisfies this property. **Final answer:** $x = 10$