Question

use the drop - down menus to complete the statements.
at the turn of the twentieth century, china faced several big challenges. european countries, such as great britain,
were eager to
in china. meanwhile, the power of the imperial dynasty had grown too
to deal with th olutionary groups inside china wanted more economic and political freedom for
chinese peop ps to overthrow the emperor and establish a republic.
spread democracy
reduce their role
extend their power

Explanation:

For the first drop - down: During the turn of the 20th century, European powers like Great Britain were interested in expanding their influence and power in China (through imperialism, trade, etc.). "Spread democracy" is not in line with their imperialist goals, and "reduce their role" is the opposite of what they wanted. So "extend their power" is correct.
For the second drop - down (assuming the context is about the imperial dynasty's power): The imperial dynasty's power had become too weak (since it was unable to deal with internal and external challenges). Words like "strong" would not fit as the dynasty was in decline.
For the third drop - down (about revolutionary groups): Revolutionary groups inside China wanted to take action to overthrow the emperor. So they would "work" (or a similar action - oriented word, but from the context of the options we can infer) to overthrow the emperor. But based on the first part's correct option:

Answer:

First drop - down: extend their power
(Note: For the other drop - downs, more context about the options is needed, but for the visible first drop - down with the given options, "extend their power" is the correct choice based on historical context of European imperialism in China at the turn of the 20th century.)