Question

如图,在△ABC中,∠ABD=∠CBD,BD交AC于点D,已知∠ABC=∠C=∠BDC。求∠A和∠C的度

如图,在△ABC中,∠ABD=∠CBD,BD交AC于点D,已知∠ABC=∠C=∠BDC。求∠A和∠C的度。急！~

Answer 1

∠CBD、∠C、∠BDC在同一三角形中，故相加是180°
因为∠ABD=∠CBD。所以∠CBD=1/2∠ABC
因为∠ABC=∠C=∠BDC 所以∠CBD=1/2∠C=1/2∠BDC
所以∠CBD+∠C+∠BDC=∠CBD+2∠CBD+2∠CBD=180°
所以∠CBD=36°，∠ABC=∠C=2*36°=72°
则∠A=180°-∠ABC-∠C=36°

Answer 2

∵∠ABC=∠C=∠CBD
又因为∠ABD=∠CBD
而∠ABD+∠CBD=∠ABC
∴∠ABD+∠CBD=∠C=∠BDC,∠C=2∠CBD=∠BDC
∵∠DBC+∠C+∠BDC=5∠CBD=180°
∴∠CBD=36°
∴∠C=36°×2=72°
∴∠ABC=36°+36°=72°
∵∠A+∠ABC+∠C=180°
∴∠A=180°-72°-72°=36°