Question

如图,AB=AC,P、O在AB、AC上,AP=PQ=QB=BC,则∠A大小为?？

Answer 1

有点小难度,参考了别的题目.
过点B作PQ的平行线,过点P作AB的平行线,两条平行线相交于点D,连接CD
∴四边形BQPD是平行四边形
∵QB = QP
∴平行四边形BQPD是菱形
∴PD=PQ = AP,
∠QBD = ∠QPD
∵PDAB
∴∠CPD = ∠A = ∠QPD
∴∠A = ∠QBD
∵AC = AB,AP = BQ
∴△PDC≌△APQ
∴CD = PQ,∠AQP=∠PCD
∵AQ = QP
∴∠A = ∠AQP
∴∠A = ∠QBD = ∠PCD
∵PQ = PD=DB = BC
∴△DBC是等边三角形
∴∠DBC+∠DCB = 120°
∴3∠A + ∠DBC+∠DCB=180°
∴∠A = 20°
,1,