A B727 DEP DCA WAS GIVEN A HDG OF 215 DEGS TO FLY BY IAD DEP CTLR. CTLR CALLS FLT AND WANTS TO KNOW WHY THEY ARE ON THAT HDG. CTLR WANTED THEM ON A 315 DEG HDG.

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DEPARTING NW FROM DCA 328 DEG RADIAL; NOISE ABATEMENT DEP. NATIONAL DEP HANDED US OFF TO DULLES RADAR FOR VECTORS; J211. CTLR GAVE US A HDG OF 215 DEGS. THE COPLT AND I BOTH DIALED 215 DEGS IN OUR HDG BUG. WE BOTH DID THIS INDEPENDENTLY. THE CTLR ASKED US AFTER ROLLING OUT ON THE HDG WHAT OUR HDG WAS. WE RESPONDED 215 DEGS ASSIGNED. THE CTLR RESPONDED; YOU SHOULD PAY ATTN TO THE CTLR. THE COPLT READ BACK THE HDG ISSUED OF 215 DEGS. THE CTLR WAS VERY BUSY AND WAS SENDING ACFT BEHIND US ON THAT HDG. IT APPEARED THAT HE HAD US MIXED UP WITH OTHER DEPS. NO TFC CONFLICT RESULTED AS A RESULT OF THIS MISCOM. THE CTLR APPARENTLY THOUGHT HE GAVE US A HDG OF 315 DEGS. SUPPLEMENTAL INFO FROM ACN 419474: AS WE ROLLED OUT ON 215 DEG HDG; DEP QUERIED US ON OUR HDG. WHEN I SAID '215 DEGS' HE SAID 'XXXX PAY ATTN; TURN IMMEDIATELY TO HDG 315 DEGS.' IT WAS OBVIOUS TO US THAT WE HAD BEEN ISSUED THE WRONG HDG. THE CTLR OBVIOUSLY FELT THAT WE WERE AT FAULT. THE CTLR MAY HAVE MISTAKENLY GIVEN US A HDG OF 215 DEGS AS HE HAD ISSUED THE SAME HDG TO SEVERAL ACFT AHEAD OF US. WE; AS A CREW; MIGHT HAVE NOTICED THAT THIS HDG WAS IN THE WRONG DIRECTION FOR OUR RTE OF FLT. WE DID NOT QUESTION THE CTLR THOUGH.