Question

【題目】如圖，平行四邊形ABCD繞點(diǎn)A逆時(shí)針旋轉(zhuǎn)30°，得到平行四邊形AB′C′D′，點(diǎn)B′恰好落在BC邊土，B′C′和CD交于點(diǎn)P，則∠B′PD的度數(shù)是（　　）

A. 105° B. 120° C. 130° D. 135°

Answer 1

【答案】D

【解析】

根據(jù)旋轉(zhuǎn)的性質(zhì)得出AB=AB' , ∠BAB' =30°,進(jìn)而得出∠B的度數(shù), 再利用平行四邊形的性質(zhì)得出∠C的度數(shù)，可得∠B′PD的度數(shù).

解：平行四邊形ABCD繞點(diǎn)A逆時(shí)針旋轉(zhuǎn)30,得到平行四邊形AB'C'D'(點(diǎn)B'與點(diǎn)B是對應(yīng)點(diǎn),點(diǎn)C與點(diǎn)C是對應(yīng)點(diǎn),點(diǎn)D'與點(diǎn)D是對應(yīng)點(diǎn)),

AB=AB',∠BAB'=30°, ∠CB' C'=30°,

∠B=∠AB'B=(180°-30°)/2=75°,

∠C=180°-75° =105°，

∠B′PD=∠CB' C'+∠C=30°+105°=135°

故選D.