A1. What is the size of the central angle corresponding to a circular arc that has the same length as the radius of the circle?
(A) $\frac{45^{\circ}}{\pi}$
(B) $\frac{90^{\circ}}{\pi}$
(C) $\frac{135^{\circ}}{\pi}$
(D) $\frac{180^{\circ}}{\pi}$
(E) $\frac{270^{\circ}}{\pi}$
A1. The length of a circular arc is calculated using the formula $l=\frac{\pi r \alpha}{180^{\circ}}$. Since the length of the circular arc is equal to the radius of the circle, we rearrange the equation to $r=\frac{\pi r \alpha}{180^{\circ}}$. From the equation, we express $\alpha$ and get the result $\frac{180^{\circ}}{\pi}$.