∵∠ADP=∠CBP,∠ADP=∠CDP
∴四边形ABPD 38°+∠ADP+∠ADP+X=360° ①
∴四边形CBPD 46°+∠CBP+∠CDP+360°-X=360° ②
∴②-①
368°-2X=0
X=184°
∴∠BPD=184°