Segment AD-bisector of triangle ABC. A straight line is drawn through point D, intersecting the side AB

Segment AD-bisector of triangle ABC. A straight line is drawn through point D, intersecting the side AB at point E so that AE = ED. Find the angles of the triangle AED if the angle BAC = 64 degrees.

Let’s deal with this task.
Given:
ABC – triangle
AD – bisector
AE = ED
∠BAC = 64 °.
To find:
Angles of triangle AED.
Decision:
Since AO is a bisector, then ∠ЕАD = 32 °
We know that AE = ED, so triangle AED is isosceles, therefore, in an isosceles triangle, all angles at the base are equal.
∠ЕАD = ∠АDE = 32 °
Now we find the angles of the triangle AED:
180 ° -64 ° = 116 °
Answer: ∠ЕАD = 32 °, ∠АDE = 32 °, ∠АЕD = 116 °