1. **State the problem:** We need to find the angle in degrees of the shaded portion of a circle divided into 10 equal sectors, with 7 sectors shaded. 2. **Formula and rules:** The total angle in a circle is $360^\circ$. 3. **Calculate the angle of one sector:** Since the circle is divided into 10 equal sectors, each sector has an angle of $$\frac{360^\circ}{10} = 36^\circ.$$ 4. **Calculate the angle of the shaded portion:** There are 7 shaded sectors, so the total shaded angle is $$7 \times 36^\circ = 252^\circ.$$ 5. **Final answer:** The angle of the shaded portion of the circle is **$252^\circ$**.