8,9 One of the angles formed by the intersecting lines $a$ and $b$ is $15^{\circ}$. Line $a_{1}$ is symmetric to line $a$ with respect to line $b$, and line $b_{1}$ is symmetric to line $b$ with respect to $a$. Find the angles formed by the lines $a_{1}$ and $b_{1}$.
Let's take points $A$ and $B$, different from $O$, on the lines $a$ and $b$ respectively, which intersect at point $O$. Suppose $\angle A O B=15^{\circ}$. The point $A_{1}$, symmetric to point $A$ with respect to line $b$, lies on line $a_{1}$, and $\angle A_{1} O B = \angle A O B = 15^{\circ}$.

The point $B_{1}$, symmetric to point $B$ with respect to line $a$, lies on line $b_{1}$, and $\angle B_{1} O A = \angle B O A = 15^{\circ}$. Since ray $O B$ lies between rays $O A_{1}$ and $O A$, and ray $O A$ lies between $O B$ and $O B_{1}$, then $\angle A_{1} O B_{1} = \angle A_{1} O B + \angle A O B + \angle A O B_{1} = 15^{\circ} + 15^{\circ} + 15^{\circ} = 45^{\circ}$

## Answer

$45^{\circ}, 45^{\circ}, 135^{\circ}, 135^{\circ}$.