已知AB=A1B,A1C=A1A2,A2D=A2A3,A3E=A3A4,∠B=20°.
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已知AB=A1B,A1C=A1A2,A2D=A2A3,A3E=A3A4,∠B=20°.
(1)求∠A4的度数;
(2)根据上面的规律,请写出∠An的度数.(用含n的代数式表示)
![](http://img.wesiedu.com/upload/5/2f/52f8ebdbcac4d6dd7417d3ffce22bad3.jpg)
(1)求∠A4的度数;
(2)根据上面的规律,请写出∠An的度数.(用含n的代数式表示)
![](http://img.wesiedu.com/upload/5/2f/52f8ebdbcac4d6dd7417d3ffce22bad3.jpg)
![已知AB=A1B,A1C=A1A2,A2D=A2A3,A3E=A3A4,∠B=20°.](/uploads/image/z/19371925-37-5.jpg?t=%E5%B7%B2%E7%9F%A5AB%3DA1B%2CA1C%3DA1A2%2CA2D%3DA2A3%2CA3E%3DA3A4%2C%E2%88%A0B%3D20%C2%B0.)
1、∵AB=A1B,∠B=20°
∴∠A=∠BA1A=(180°-20°)/2=80°
∴∠CA1A2=180°-80°=100°
∵A1C=A1A2
∴∠CA2A1=(180°-100°)/2=40°
∴∠DA2A3=180°-40°=140°
∵A2D=A2A3
∴∠DA3A2=(180°-140°)/2=20°
∴∠EA3A4=180°-20°=160°
∵A3E=A3A4
∴∠A4=(180°-160°)=10°
2、A1=80°/2^0
A2=80°/2^1
A3=80°/2²
A4=80°/2³
An=80°/2^(n-1)
∴∠A=∠BA1A=(180°-20°)/2=80°
∴∠CA1A2=180°-80°=100°
∵A1C=A1A2
∴∠CA2A1=(180°-100°)/2=40°
∴∠DA2A3=180°-40°=140°
∵A2D=A2A3
∴∠DA3A2=(180°-140°)/2=20°
∴∠EA3A4=180°-20°=160°
∵A3E=A3A4
∴∠A4=(180°-160°)=10°
2、A1=80°/2^0
A2=80°/2^1
A3=80°/2²
A4=80°/2³
An=80°/2^(n-1)
如图所示,已知:∠B=20°,AB=A1B,A1C=A1A2,A2D=A2A3,A3E=A3A4,.,则∠An= 度.
如图所示,已知∠B=20°,AB=A1B,A1C=A1A2,A2D=A2A3,A3E=A3A4,则∠An=
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