國二算角度的題目一題

還好啦!圖不錯啊!

Ans:設角DBC=a，角ADC=r，角ACB=180-2r

1. 20+3a=30+r=外角
2. 180-2r=4a(等腰)

聯立後解出a=20，r=50

角BAC=180-80*2=20

!!拜託把我選為最佳答案!!我可是拿著紙拼命算呢!!

設∠DBC=X度∠DCE=Y度則∠ACB=∠ABC=4X度
X+4X+30+Y=180 5X+Y=150 ------(1)
4X+2Y=180 2X+Y=90--------(2)
(1)-(2)
3X=60 X=20
∠ACB+∠ABC=8X度=160度
∠BAC=180-160=20度

given that∠DBC=1/4∠ABC
in △ABC,
when AB=AC
so ∠ABC=∠ACB(base ∠s,isos △)
iq.∠BAC=180-2∠ABC(∠ sum of △)
in △BCD
∠DBC+∠BDC+∠DCB=180(∠sum of △)
5/4∠ABC+∠ACD=150
when 2∠ACD=∠ABC+∠BAC(ext ∠ of △)
so 2∠ACD=180-∠ABC
after than,when 5/4∠ABC+∠ACD=150
iq. 5/4∠ABC+(180-∠ABC)/2=150
5∠ABC+360-2∠ABC=600
3∠ABC=240
∠ABC=80
so ∠BAC
=180-2(80)
=20

2011-03-28 06:50:10 補充：
that's a good way to using liner equation...