548. Which special angles can be divided into 3 equal parts using a compass and a straightedge?
548. All angles of the form $3 \alpha$, where $\alpha$ denotes an angle that can be constructed with a compass and straightedge (see question 481). Since we can construct angles of $60^{\circ}, 45^{\circ}, 30^{\circ}, 2 \frac{1}{2}^{\circ}, 15^{\circ}, 71^{\circ}, \ldots 37 \frac{1}{2}^{\circ}$, $52 \frac{1}{2}^{\circ}, \ldots$ we will be able to divide into three parts angles of: $180^{\circ}, 135^{\circ}, 90^{\circ}$, $67 \frac{1}{2}^{\circ}, 45^{\circ}, 22 \frac{1}{2}^{\circ}, \ldots 107 \frac{1}{2}^{\circ}, 157 \frac{1}{2}^{\circ} \ldots$