GIVEN A TURN AND NEW HDG CLRNC; FLC READ BACK THE NEW HDG (BOTH PLTS HEARD 170 DEGS); BUT THE TRACON CTLR MISSED THE READBACK AND THEN; WHEN NOTING THE ACFT WAS CONTINUING A R TURN; QUESTIONED THEM AND INTERVENED WITH THE CORRECT HDG.

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WE WERE ON A VECTOR FOR APCH TO RWY 24R ILS. WE WERE ON A HDG OF 050 DEGS APPROX 15 MI E OF LAX. THIS DISTANCE IS USUALLY PAST THE POINT AT WHICH WE ARE TURNED ONTO THE APCH. TFC WAS BACKED UP AND WE WERE HOLDING MINIMUM SPD TO STILL ALLOW A 30 DEG ANGLE OF BANK ASSIGNED 150 KTS. WE WERE GIVEN INSTRUCTIONS BY APCH CTL TO TURN R TO (WHAT WE THOUGHT) A HDG OF 170 DEGS. I HEARD 170 DEGS (I WAS FLYING) AND THE FO HEARD AND READ BACK 'TURN R TO A HDG OF 170 DEGS.' A FEW SECONDS LATER; APCH CTL ASKED US WHAT OUR HDG WAS. THE FO RESPONDED TURNING R THROUGH 150 DEGS FOR 170 DEGS. APCH CTL INSTRUCTED US TO TURN BACK TO A HDG OF 070 DEGS IMMEDIATELY THAT WE WERE NOT TO TURN TO 170 DEGS. WE IMMEDIATELY TURNED L (30 DEG ANGLE OF BANK) TO HDG 070 DEGS. NO FURTHER OCCURRENCES WERE EXPERIENCED. AFTER THE FLT HAD TERMINATED; THE FO AND I WERE DISCUSSING THE INSTRUCTIONS AND WE STILL FEEL WE HEARD 170 DEGS. I KNOW APCH CTL AT LAX CAN GET VERY HECTIC BUT THAT SHOULD INDICATE TO THE CTLR TO SPEAK INSTRUCTIONS CLRLY AND LISTEN FOR THE READBACK. AFTER ALL; THAT IS WHY WE READ BACK INSTRUCTION.