We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots ( ℓ + 1 ) 2 or ( ℓ + 1 ) 1 , that are the closure of the rational ( 2 ℓ − 1 ) / ( ℓ − 1 ) -tangles or ( 2 ℓ − 1 ) / ℓ -tangles, respectively.