Math~~

2007-12-08 1:42 pm
Figure shows a regular pentagon.
The diagonals AC and BD intersect at P.
(a) Find ∠ABD.
(b) Find ∠APD.
更新1:

Figure http://img516.imageshack.us/img516/649/46880293ki7.jpg

回答 (1)

2007-12-08 3:15 pm
✔ 最佳答案
五邊形每一隻角:(5-2)x180度/5 = 108度
考慮三角形BCD,
CD=CB
是一個等腰三角形
∠CDB=(180度-108度)/2
∠CDB=36度
考慮梯形ABDE
∠ABD=360度-∠BAE-∠AED-∠EDB
∠ABD=360度-108度-108度-(108度-∠CDB)
∠ABD=360度-108度-108度-(108度-36)
∠ABD=72度
考慮三角形ABC
AB=BC
是一個等腰三角形
∠BAC=(180度-108度)/2
∠BAC=36度
考慮四邊形APDE
∠APD=360度-∠PAE-∠AED-∠EDP
∠APD=360度-(108度-∠BAC)-108度-(108度-∠BDC)
∠APD=360度-(108度-36度)-108度-(108度-36度)
∠APD=108度


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