A method for processing a transparent workpiece, the method comprising: directing a laser beam in a first orientation along a first beam pathway into the transparent workpiece, the laser beam passing through an impingement surface of the transparent workpiece at an impingement location, wherein: a first portion of the laser beam directed into the transparent workpiece comprises a first laser beam focal line and generates an induced absorption to produce a first defect segment within the transparent workpiece; and adjusting the laser beam to a second orientation along a second beam pathway such that the laser beam passes through the impingement surface at a second impingement location to enter the transparent workpiece, wherein: a second portion of the laser beam directed into the transparent workpiece comprises a second laser beam focal line and generates the induced absorption to produce a second defect segment within the transparent workpiece, wherein: each of the first and second laser beam focal lines (113A, 113B) comprise a circular angular spectrum within the transparent workpiece; and at least one of the first laser beam focal line and the second laser beam focal line comprise an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location, wherein each of the first and second laser beam focal lines (113A, 113B) comprise: a wavelength λ; a spot size w o; and a Rayleigh range Z R that is greater than F D = πw o 2 λ, where F D is a dimensionless divergence factor comprising a value of 10 or greater. directing a laser beam in a first orientation along a first beam pathway into the transparent workpiece, the laser beam passing through an impingement surface of the transparent workpiece at an impingement location, wherein: a first portion of the laser beam directed into the transparent workpiece comprises a first laser beam focal line and generates an induced absorption to produce a first defect segment within the transparent workpiece; and adjusting the laser beam to a second orientation along a second beam pathway such that the laser beam passes through the impingement surface at a second impingement location to enter the transparent workpiece, wherein: a second portion of the laser beam directed into the transparent workpiece comprises a second laser beam focal line and generates the induced absorption to produce a second defect segment within the transparent workpiece, wherein: each of the first and second laser beam focal lines (113A, 113B) comprise a circular angular spectrum within the transparent workpiece; and at least one of the first laser beam focal line and the second laser beam focal line comprise an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location, each of the first and second laser beam focal lines (113A, 113B) comprise a circular angular spectrum within the transparent workpiece; and at least one of the first laser beam focal line and the second laser beam focal line comprise an internal focal line angle of greater than 10° relative to a plane orthogonal to the impingement surface at the impingement location, a wavelength λ; a spot size w o; and a Rayleigh range Z R that is greater than F D = πw o 2 λ, where F D is a dimensionless divergence factor comprising a value of 10 or greater.