与角平分线有关的几何问题在各类考试(竞赛和中考)中屡见不鲜,解决这类问题时,若能通过巧添辅助线构造全等三角形常可使问题化难为易.例1如图,在△ABC中,∠BAC的平分线交BC于D,AC=AB+BD,∠C=30°,则∠ABC的度数是(江苏省初中数学竞赛题)()A.45°B.60°C.75°D.90°解:延长AB到E Geometry problems related to the angle bisector are common in all kinds of examinations (competitions and high school entrance examinations). When solving such problems, it can often be difficult to construct problems by constructing the equal triangles through the auxiliary lines. Example 1 In △ABC, the bisecting line of ∠BAC intersects BC in D, AC=AB+BD, and ∠C=30°, then the degree of ∠ABC is (Junior Junior High School Mathematics Competition Question)()A.45°B.60 °C.75°D.90° Solution: Extend AB to E