1. The problem asks to find the number of symmetry lines of a figure that is a circle divided into eight triangular sectors by radial lines. 2. A circle itself has infinite lines of symmetry, but when divided into sectors, the symmetry lines depend on the number and arrangement of these sectors. 3. Since the circle is divided into 8 equal triangular sectors, the figure has rotational symmetry of order 8. 4. Each sector corresponds to an angle of $\frac{360^\circ}{8} = 45^\circ$. 5. The symmetry lines will be those that pass through the center and either bisect the sectors or pass along the boundaries between sectors. 6. For an even number of sectors, the number of symmetry lines equals the number of sectors, which is 8. 7. Therefore, the figure has 8 lines of symmetry.