Median AD of triangle ABC is extended beyond the side BC. On the continuation of the median DE

Median AD of triangle ABC is extended beyond the side BC. On the continuation of the median DE, point E is taken so that DE = AD, and point E is connected to point C. Find the angle ACE if the angle ACD = 56 °, the angle ABD = 40 °

1. Triangles ADB and EDC are equal by the first sign of equality of triangles:

CD = BD because AD is the median of triangle ABC;

AD = ED by the condition of the problem;

∠ADB = ∠EDC as vertical angles.

2. From the equality of the triangles, the equality of the corresponding angles follows:

∠ECD = ∠ABD = 40 °.

Hence:

∠ACE = ∠ACD + ∠ECD = 56 ° + 40 ° = 96 °.

Answer: 96 °.