The option that offers the best analysis of why the US entered World War I is:
c. the US was angered by German unrestricted submarine warfare.
While the assassination of Archduke Franz Ferdinand (option a) was a significant event that triggered the war in Europe, it was not the direct reason for the US entry into the conflict. The actions of the Triple Alliance and the Triple Entente (options b and d) pertained more to the dynamics of the war among European powers rather than the US involvement.
The German policy of unrestricted submarine warfare, particularly the sinking of ships like the Lusitania, angered the American public and government, leading to a shift in sentiment toward joining the war. This option directly addresses the factors that influenced the US decision to enter World War I.