The median BO of the triangle ABC is extended on the basis of AC for the segment BO = OD and point D is connected

The median BO of the triangle ABC is extended on the basis of AC for the segment BO = OD and point D is connected to point A. Find the angle ВAD if the angle BAO = 52 degrees and the angle BCO = 44 degrees.

Consider the triangles BOC and DOA, in them:
BO = OD (by condition);
AO = OС (ВO – conditional median);
∠VOC = ∠DOA (vertical).
We get the first sign of equality of triangles (two sides and the angle between them).
From the equality of the triangles we have:
∠ ВСО = ∠DAO = 44 °.
Find the degree measure of the angle BAD:
∠ BAD = ∠ BAO + ∠DAO = 52 ° + 44 ° = 96 °.
Answer: The BAD angle is 96 °.