A combustor is provided for a turbine engine. The combustor includes a first liner having a first side and a second side and a second liner having a first side and a second side. The second side of the second liner forms a combustion chamber with the second side of the first liner, and the combustion chamber is configured to receive an air-fuel mixture for combustion therein. The first liner defines a plurality of effusion cooling holes configured to form a film of cooling air on the second side of the first liner. The plurality of effusion cooling holes including a first effusion cooling hole extending from the first side to the second side with a non-linear line of sight.