Two round trip tickets, transiting in Chengdu airport

Hi, I am flying from the US to Nepal. However it was not possible for me to book that trip on one itinerary. So, I booked two round-trip flights.
1) US to Chengdu (round trip)
- US --> Chengdu Aug 10 (itinerary 1)
- Chengdu --> Nepal Aug 11 (itinerary 2)

2) Chengdu to Nepal (round trip)
- Nepal --> Chengdu Aug 19 (itinerary 2)
- Chengdu --> US Aug 20 (itinerary 1)

Do I qualify for the 72 hour visa-free entry?

Thanks