Strictly systolic angled complexes and hyperbolicity of one-relator groups

We introduce the notion of strictly systolic angled complexes. They generalize Januszkiewickz and \'Swi\k{a}tkowski's $7$-systolic simplicial complexes also their metric counterparts, which appear as natural analogues to Huang Osajda's metrically in context negative curvature. prove that groups act on them geometrically, together with finitely presented subgroups, are hyperbolic. use these study geometry one-relator without torsion, hyperbolicity such under a small cancellation hypothesis, weaker than $C'(1/6)$ $C'(1/4)-T(4)$.