如图,∠ACD是△ABC的外交,∠ABC的平分线和∠ACD的平分线交于点A,∠A1BC的平分线与∠A1CD的平分线交于点A2,…,∠An-1BC的平分线与∠An-1CD的平分线交于点An.设∠A=θ :则(1)求∠A1的度数(2)求
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![如图,∠ACD是△ABC的外交,∠ABC的平分线和∠ACD的平分线交于点A,∠A1BC的平分线与∠A1CD的平分线交于点A2,…,∠An-1BC的平分线与∠An-1CD的平分线交于点An.设∠A=θ :则(1)求∠A1的度数(2)求](/uploads/image/z/1648902-30-2.jpg?t=%E5%A6%82%E5%9B%BE%2C%E2%88%A0ACD%E6%98%AF%E2%96%B3ABC%E7%9A%84%E5%A4%96%E4%BA%A4%2C%E2%88%A0ABC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E5%92%8C%E2%88%A0ACD%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%BA%8E%E7%82%B9A%2C%E2%88%A0A1BC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%B8%8E%E2%88%A0A1CD%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%BA%8E%E7%82%B9A2%2C%E2%80%A6%2C%E2%88%A0An-1BC%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%B8%8E%E2%88%A0An-1CD%E7%9A%84%E5%B9%B3%E5%88%86%E7%BA%BF%E4%BA%A4%E4%BA%8E%E7%82%B9An%EF%BC%8E%E8%AE%BE%E2%88%A0A%3D%CE%B8+%EF%BC%9A%E5%88%99%EF%BC%881%EF%BC%89%E6%B1%82%E2%88%A0A1%E7%9A%84%E5%BA%A6%E6%95%B0%EF%BC%882%EF%BC%89%E6%B1%82)
如图,∠ACD是△ABC的外交,∠ABC的平分线和∠ACD的平分线交于点A,∠A1BC的平分线与∠A1CD的平分线交于点A2,…,∠An-1BC的平分线与∠An-1CD的平分线交于点An.设∠A=θ :则(1)求∠A1的度数(2)求
如图,∠ACD是△ABC的外交,∠ABC的平分线和∠ACD的平分线交于点A
,∠A1BC的平分线与∠A1CD的平分线交于点A2,…,∠An-1BC的平分线与∠An-1CD的平分线交于点An.设∠A=θ :则(1)求∠A1的度数(2)求∠A2的度数(3)猜想∠An等于多少?
如图,∠ACD是△ABC的外交,∠ABC的平分线和∠ACD的平分线交于点A,∠A1BC的平分线与∠A1CD的平分线交于点A2,…,∠An-1BC的平分线与∠An-1CD的平分线交于点An.设∠A=θ :则(1)求∠A1的度数(2)求
(1)∵∠A+∠ABC+∠ACB=180∴∠ABC+∠ACB=180-∠A∵∠ACD=180-∠ACB,CA1平分∠ACD∴∠A1CD=∠ACD/2=(180-∠ACB)/2=90-∠ACB/2∵BA1平分∠ABC∴∠A1BC=∠ABC/2∵∠A1CD是△A1BC的外角∴∠A1CD=∠A1+∠A1BC=∠A1+∠ABC/2∴∠A1+∠ABC/2=90-∠ACB/2∴∠A1=90-(∠ABC+∠ACB)/2=90-(180-∠A)/2=∠A/2
(2)同理可得:∠A2=∠A1/2=∠A/4∠A2=∠A/2²
(3)依次类推:∠An=∠A/2 ⁿ
1)∠A1 = 180°- ∠B/2 - ((180°-∠C)/2 + ∠C) = 1/2*(180°-∠B-∠C) = 1/2∠A = 1/2θ
2)同理∠A2 = 1/2∠A1 = 1/4θ
3)∠An = 1/(2^n)θ