设∠A=x，∵AP1=P1P2=P2P3=…=P7P8，∴∠A=∠AP2P1=x，∴∠P2P1P3=2x，∴∠P3P2P4=3x，…，∠P7P6P8=∠P8P9P7=8x，∴∠AP7P8=7x，∠AP8P7=9x，在△AP7P8中，∠A+∠AP7P8+∠AP8P7=180°，即x+8x+9x=180°，解得x=10°，即∠A=10°．故答案为10°．
