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歡迎您訪問數學考題練習:如圖,兩平面鏡所成的∠1,一束光線由是P發出,!

數學考題練習:如圖,兩平面鏡所成的∠1,一束光線由是P發出,

更新時間:2024-01-12 16:45:37作者:貝語網校

如圖,兩平面鏡所成的∠1,一束光線由是P發出,經平面鏡OB,OA兩次反射后回到點P,已知PQ∥OA,PR∥OB,則∠1的度數為

A.30°

B.45°

C.60°

D.75°

試題答案

C

試題解析

根據平行線得出∠BQP=∠1,∠PRA=∠1,根據入射角等于反射角,得出∠BQP=∠OQR,∠PRA=∠ORQ,推出∠1=∠OQR=∠ORQ,根據三角形的內角和定理求出∠1即可.

解答:∵PQ∥OA,PR∥OB,

∴∠BQP=∠1,∠PRA=∠1,

∵入射角等于反射角,

∴∠BQP=∠OQR,∠PRA=∠ORQ,

∴∠1=∠OQR=∠ORQ,

∴由三角形的內角和定理得:3∠1=180°,

∴∠1=60°,

故選C.

點評:本題考查了平行線的性質和三角形的內角和定理的應用,關鍵是根據已知得出∠1=∠OQR=∠ORQ,主要考查了學生運用定理進行推理的能力.

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