Question

如圖，已知AB∥CD，BE平分∠ABC，∠CDE＝150°，則∠C的度數是

1. A.
   100°
2. B.
   110°
3. C.
   120°
4. D.
   150°

Answer 1

C
∵直線AB∥CD，∴∠CDB=∠ABD，
∵∠CDB=180°-∠CDE=30°，∴∠ABD=30°，
∵BE平分∠ABC，∴∠ABD=∠CBD，∴∠ABC=∠CBD+∠ABD=60°，
∵AB∥CD，∴∠C=180°-∠ABC=180°-60°=120°．故選C．