In the diagram, points $P_{1}, P_{3}, P_{5}, P_{7}$ are on $B A$ and points $P_{2}, P_{4}, P_{6}, P_{8}$ are on $B C$ such that $B P_{1}=P_{1} P_{2}=P_{2} P_{3}=P_{3} P_{4}=P_{4} P_{5}=P_{5} P_{6}=P_{6} P_{7}=P_{7} P_{8}$. If $\angle A B C=5^{\circ}$, what is the measure of $\angle A P_{7} P_{8}$ ?

![](https://cdn.mathpix.com/cropped/2024_04_17_56af4dba662dd63eccc5g-1.jpg?height=225&width=873&top_left_y=1606&top_left_x=672)