Question

【題目】如圖，已知∠AOB=120°，點(diǎn)A繞點(diǎn)O順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A1落在射線OB上，點(diǎn)A繞點(diǎn)A1順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A2落在射線OB上，點(diǎn)A繞點(diǎn)A2順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A3落在射線OB上，…，連接AA1，AA2，AA3…，依此作法，則∠AAnAn+1等于______度．（用含n的代數(shù)式表示，n為正整數(shù)）

Answer 1

【答案】.

【解析】∵點(diǎn)A繞點(diǎn)O順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A1落在射線OB上，

∴OA=OA1，

∴∠AA1O=，

∵點(diǎn)A繞點(diǎn)A1順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A2落在射線OB上，

∴A1A=A1A2，

∴∠AA2A1=∠AA1O=，

∵點(diǎn)A繞點(diǎn)A2順時針旋轉(zhuǎn)后的對應(yīng)點(diǎn)A3落在射線OB上，

∴A2A=A2A3，

∴∠AA3A2=∠AA2A1=，

∴∠AAnAn﹣1=，

∴∠AAnAn+1=180°﹣．

故答案是：180﹣．