A C172 pilot entering the pattern at a non towered airport reported a NMAC with traffic on downwind.

Narrative

I was approaching ZZZ from the north; made CTAF report 5nm out; intending to join Left downwind for Rwy XX. I displaced myself 2nm east of the airport; intending to fly just south the airport; then make a right turn to join downwind Rwy XX at a 45 angle leg. As I was abeam the airport; I heard a traffic report from an aircraft inbound from east; hence was busy looking to my left (eastward) for that traffic. However; because of this distraction; I failed to recognize a departing traffic announcing it's turning crosswind Rwy XX. Halfway through my right turn; I heard the departing traffic announcing it's now on downwind Rwy XX. A moment later I saw the downwind traffic to my left side; about 1/3-1/4 mile; 100 ft higher. I immediately took an evasive action and made a moderate dive to increase separation; before reversing the turn and headed back East to get away from the traffic pattern; then re-joined later when the pattern quieted down.I believe in hindsight; I was too close to the airport and almost in the pattern when I flew south; I should have displaced further to the East (5nm or so) before attempting turn and join the traffic patter. Also; I should have listened longer to establish a visual picture of all the pattern traffics before attempting to join. In addition; equipping myself with an ADSB-in with screen display of traffic would also further prevent near-miss like this from happening again.