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A market research survey of a group of consumers is represented in a pie chart. The respondents are classified into four categories: A, B, C, and D. Category A corresponds to a sector with an angle of 108^\\circ. Category B represents of the total respondents. Category C has a frequency that is twice that of Category D. If there are 180 more respondents in Category B than in Category D, what is the total number of respondents surveyed?
A market research survey of a group of consumers is represented in a pie chart. The respondents are classified into four categories: A, B, C, and D. Category A corresponds to a sector with an angle of 108^\\circ. Category B represents of the total respondents. Category C has a frequency that is twice that of Category D. If there are 180 more respondents in Category B than in Category D, what is the total number of respondents surveyed?