How did Afghanistan acquire the Wakhan Corridor?

Answer 1

The Wakhan Corridor ... is a narrow (in some places less than 10 mi. wide) corridor in the Badakhshan province of Afghanistan. It is located in the Pamir mountain region, with Tajikistan to the north, Pakistan-administered Kashmir to the south and China to the east. It was created at the end of 19th century by the British Empire, to act as a buffer against potential Russian ambitions in India during the Great Game.

Answer 2

It's a relic from when Afghanistan was part of the British Empire. The British created the corridor as a buffer zone between Russia and India, which then also was part of the British Empire.

With the changes in geo-politics since then, it's now Tajikstan to the north of the corridor, and Pakistan to the south.