A combustor assembly comprising: a combustor liner defining a combustion chamber there within; and a transition piece comprising a forward portion coupled to said combustion liner and an aft portion extending from said forward portion, said aft portion comprising a transition piece frame, said transition piece frame comprising: an upstream surface, a downstream surface, and a radially inner surface extending between said upstream and downstream surfaces (98, 100), said radially inner surface comprises a leading edge extending between said radially inner surface and said upstream surface; and a plurality of cooling passages (132, 134, 144) extending from said upstream surface to said downstream surface, wherein the plurality of cooling passages comprises at least one first cooling passage oriented at a second oblique angle with respect to said leading edge, characterized in that said transition piece frame further comprises at least one third cooling passage oriented at a third oblique angle with respect to said leading edge and in a mirrored relationship with the at least one first cooling passage, the third oblique angle being different than the second oblique angle and at least one second cooling passage oriented substantially perpendicularly to said leading edge. a combustor liner defining a combustion chamber there within; and a transition piece comprising a forward portion coupled to said combustion liner and an aft portion extending from said forward portion, said aft portion comprising a transition piece frame, said transition piece frame comprising: an upstream surface, a downstream surface, and a radially inner surface extending between said upstream and downstream surfaces (98, 100), said radially inner surface comprises a leading edge extending between said radially inner surface and said upstream surface; and a plurality of cooling passages (132, 134, 144) extending from said upstream surface to said downstream surface, wherein the plurality of cooling passages comprises at least one first cooling passage oriented at a second oblique angle with respect to said leading edge, characterized in that said transition piece frame further comprises at least one third cooling passage oriented at a third oblique angle with respect to said leading edge and in a mirrored relationship with the at least one first cooling passage, the third oblique angle being different than the second oblique angle and at least one second cooling passage oriented substantially perpendicularly to said leading edge. an upstream surface, a downstream surface, and a radially inner surface extending between said upstream and downstream surfaces (98, 100), said radially inner surface comprises a leading edge extending between said radially inner surface and said upstream surface; and a plurality of cooling passages (132, 134, 144) extending from said upstream surface to said downstream surface, wherein the plurality of cooling passages comprises at least one first cooling passage oriented at a second oblique angle with respect to said leading edge, characterized in that said transition piece frame further comprises at least one third cooling passage oriented at a third oblique angle with respect to said leading edge and in a mirrored relationship with the at least one first cooling passage, the third oblique angle being different than the second oblique angle and at least one second cooling passage oriented substantially perpendicularly to said leading edge.