Question

如图,已知∠A=∠1,∠2=∠3,∠4=∠5,∠6=∠C∠ABC,求∠A的大小

Answer 1

∵ ∠A = ∠1

∴ ∠2 = ∠A + ∠1

= 2∠A

∵ ∠3 = ∠2 = 2∠A

∴ ∠4 = ∠3 + ∠A

= 2∠A + ∠A

= 3∠A

∵ ∠5 = ∠4 = 3∠A

∴ ∠6 = ∠5 + ∠A

= 3 ∠A + ∠A

= 4∠A

∴ ∠C = ∠ABC = ∠6 = 4∠A

∵ 在 △ ABC 中,

∴∠A + ∠C + ∠ABC = 180°

∴ ∠A + 4∠A + 4∠A = 180°

9 ∠A = 180°

∠A = 20°