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 Question from Caitlyn, a student: I need to find the measure of the central angle that represents the amount of time spent on each activity. My question includes a circle graph with the following: Sleep 31%, Other 15%, Entertainment 18%, Errands 7%, Work 20%, and Food 9%.

Hi Caitlyn,

Because of the symmetry of a circle the area of a sector is proportional to its central angle. Hence if you have two sectors and the area of one is half the area of the other than the central angle of the smaller sector is half the central angle of the larger sector. Conversely if the central angle of one is four times the central angle of the other then the area of the larger sector is four times the area of the small sector.

In general if the area of a sector is $k\%$ of the area of the circle then the central angle of the sector is $k\%$ of the entire central angle of $360^o$.

Penny

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