Question 15
Three cars depart from a city $A$ at the same time and travel a closed path consisting of three line segments $AB$, $BC$ and $CA$. The speeds of the first car on these segments are 12, 10 and 15 kilometers per hour, respectively. The speeds of the second car are 15, 15 and 10 kilometers per hour, respectively. Finally, the speeds of the third car are 10, 20 and 12 kilometers per hour, respectively. Find the value of angle $\angle ABC$, knowing that all three cars end in the city $A$ at the same time.