Occasionally, Martin Luther King Jr. Day falls on Inauguration Day, but the two dates are not directly related. But why this day, and why does it share the day with Martin Luther King Jr. Day? Inauguration Day and the 20th AmendmentJanuary 20 is observed as Inauguration Day because of the 20th Amendment. Martin Luther King Jr. Day is a federal holiday that celebrates the life and legacy of civil rights leader Dr. Martin Luther King Jr. Occasionally, Martin Luther King Jr. Day falls on Inauguration Day.