1. The problem asks to rotate the angle $-526^\circ$ to an equivalent angle within $10^\circ$. 2. To find an equivalent angle within a standard range, we add or subtract full rotations of $360^\circ$ because rotating by $360^\circ$ results in the same position. 3. Start by adding $360^\circ$ to $-526^\circ$: $$-526^\circ + 360^\circ = -166^\circ$$ 4. The angle $-166^\circ$ is still less than $-10^\circ$, so add another $360^\circ$: $$-166^\circ + 360^\circ = 194^\circ$$ 5. Now, $194^\circ$ is greater than $10^\circ$, so subtract $360^\circ$ to check the other equivalent angle: $$\cancel{194^\circ} - \cancel{360^\circ} = -166^\circ$$ 6. Since neither $194^\circ$ nor $-166^\circ$ is within $\pm 10^\circ$, the closest equivalent angle within $10^\circ$ is found by considering the remainder when dividing by $360^\circ$: Calculate the remainder: $$-526^\circ \mod 360^\circ = 194^\circ$$ 7. The angle $194^\circ$ is $194^\circ - 180^\circ = 14^\circ$ away from $180^\circ$, which is not within $10^\circ$ of $0^\circ$. 8. Since the problem states "within 10°" without specifying positive or negative, the closest angle to $-526^\circ$ within $10^\circ$ is $-166^\circ$ (which is $166^\circ$ away from $0^\circ$) or $194^\circ$ (which is $14^\circ$ away from $180^\circ$). Neither is within $10^\circ$ of $0^\circ$. 9. Therefore, the equivalent angle within one full rotation closest to $-526^\circ$ is $194^\circ$. Final answer: $$\boxed{194^\circ}$$