Example 2 In $\triangle A B C$, $\angle A=70^{\circ}$, point $I$ is the incenter. Given $A C+A I=B C$. Find the degree measure of $\angle B$.

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Explanation: As shown in Figure 1, extend $C A$ to point $K$ such that $A K = A I$. Then
$$
\begin{array}{l}
C K = A C + A K \\
= A C + A I \\
= C B .
\end{array}
$$
$$
\text { Therefore, } \triangle C B I \cong \triangle C K I \text {. }
$$

Thus, $\angle C B I = \angle C K I$.
Since $A K = A I$, then $\angle C A I = 2 \angle C K I$.
Therefore, $\angle A B C = 2 \angle C B I = 2 \angle C K I = \angle C A I$ $= \frac{1}{2} \angle C A B = \frac{1}{2} \times 70^{\circ} = 35^{\circ}$.