For this case we use the following formula Area of Sector = Area * radians of sector / 2 * pi radians Where, Area: it is the area of the complete circle. We have then: Area = pi * r ^ 2 Area = pi * (6) ^ 2 Area = 36pi Substituting values: 5pi = 36pi * radians of sector / 2 * pi Clearing: radians of sector = ((5pi) * (2pi)) / (36pi) radians of sector = (10pi ^ 2) / (36pi) radians of sector = (10pi) / (36) radians of sector = (10/36) pi radians of sector = (5/18) pi in degrees: (5/18) pi * (180 / pi) = 50 degrees Answer: The measure of the central angle is: 50 degrees
