1. **State the problem:** We are given two inscribed angles in a circle, one at point U labeled $16x + 26^\circ$ and another at point R labeled $42^\circ$. We need to find the value of $x$. 2. **Recall the property of inscribed angles:** Inscribed angles that subtend the same arc are equal. Since angles at U and R are inscribed angles subtending the same arc, we set them equal: $$16x + 26 = 42$$ 3. **Solve the equation:** Subtract 26 from both sides: $$16x = 42 - 26$$ $$16x = 16$$ Divide both sides by 16: $$x = \frac{16}{16} = 1$$ 4. **Conclusion:** The value of $x$ is $1^\circ$.