Final answer:
The ideology of gentlemanly cricket aligning with the English imperial civilizing mission is true, as it aimed to teach Western values and was part of the broader Civilizing Mission ideology.
Step-by-step explanation:
The ideology of gentlemanly cricket did indeed complement the English imperial ideology of civilizing the world. This idea is a component of the broader concept of the Civilizing Mission, wherein industrialized countries, mainly in Europe and the United States, felt it their duty to bring the perceived benefits of Western culture to those they had colonized.
Sport, including cricket, was introduced to colonies with the belief that it would instill Western values such as fair play, teamwork, and competitiveness. In the context of England, cricket was seen as a way to teach gentlemanly conduct and discipline, aligning with the imperial idea that the British were a superior civilization with a moral obligation to 'civilize' their colonies. So, the statement "The ideology of gentlemanly cricket complemented the English imperial ideology of civilizing the world" is true.