Question

By the early 20th century, which country's empire encompassed one-fifth of Earth's landmass?

Answer 1

Answer: Britain

During the early 20th century, Britain was considered to be one of the most powerful and biggest empire on Earth. Almost one-fifth of the Earth's landmass is occupied or belong to Britain. The vast space that they has become a big advantage for them. 

Answer 2

The sun never sets on English soil.   Britain has colonies all over the world.  The answer is Britain.