I thought the ratio would be 5:2 since both circles had the same radius, but my textbook says it is 7:2. ???
While I agree with what you have written, one must ask whether the question was asking you to compare the area of the sectors to the total area of the circle, or whether to compare the areas of the sectors to each other. If it is the former, I would say the ratio is 7 : 2. If it is the latter I would say the ratio is 5 : 2.
You are not given the angle of the major sector for circle A.
You are given the angle of the minor sector of circle A.
The ratio of the minor sectors is 5:2 since you can fit 2 and a half minor sectors from B
into the minor sector of A.
First find the angle of the major sector of circle A.