1. **Stating the problem:** We are given that the difference between two angles $\alpha$ and $\beta$ is 26°, i.e., $\alpha - \beta = 26^\circ$. We need to find the value of $x$ given the rays and angles described. 2. **Understanding the geometry:** The three rays emanate from a point forming angles $\alpha$, $\beta$, and the two rays labeled $3x$ and $2x$. 3. **Key insight:** The rays labeled $3x$ and $2x$ form angles adjacent to $\alpha$ and $\beta$. Since these rays are adjacent and emanate from the same point, the sum of the angles around the point is 360°. 4. **Expressing $\alpha$ and $\beta$ in terms of $x$:** - The angle labeled $\alpha$ is adjacent to the ray labeled $3x$. - The angle labeled $\beta$ is adjacent to the ray labeled $2x$. From the figure description, the rays labeled $3x$ and $2x$ form angles with the horizontal ray (which is $\alpha$) and the angle $\beta$ is between the two left rays. 5. **Using the angle difference:** Given $\alpha - \beta = 26^\circ$. 6. **Relating $\alpha$ and $\beta$ to $x$:** Since the rays labeled $3x$ and $2x$ form angles adjacent to $\alpha$ and $\beta$, we can write: $$\alpha = 3x$$ $$\beta = 2x$$ 7. **Substitute into the difference equation:** $$3x - 2x = 26^\circ$$ 8. **Simplify:** $$x = 26^\circ$$ **Final answer:** $$\boxed{26^\circ}$$