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Assume the radius of the circle is r and angle of the sector Ф.
Perimeter of a sector of the circle = R.Ф
According to the question
RФ = 4xR
Ф = 4 radians.
2 π radians = 360 degrees
Ф = 4 radians = 4x360/2π = 229.29 degrees.
Hence the angle of the sector is 4 radians or 22.29 degrees.