Vincent's NT Word Studies
51. Consented (sugkatateqeimenov). Only here in New Testament.Another of Luke's numerous compounds. the Greek student will be struck with the array of compounds, from ver. 49 to 56, inclusive. The verb means to put (tiqhmi), down (kata), along with (sun). Hence to put down the same vote or opinion with another: to agree with or assent to.
Robertson's NT Word Studies
23:51 {He had not consented to their counsel and deed} (houtos ouk en sunkatateqeimenos tei boulei kai tei praxei autwn). this parenthesis is given by Luke alone and explains that, though a councillor (bouleutes, #Mr 5:43) he had not agreed to the vote of the Sanhedrin. It is fairly certain that both Joseph and Nicodemus were suspected of sympathy with Jesus and so were not invited to the trial of Jesus. {Was looking for} (prosedeceto). Imperfect middle. #Mr 15:43 has the periphrastic imperfect (en prosdecomenos).