Prove that in a regular pentagon ABCDE, the diagonals AC and AD divide the angle BAE into three equal parts.

Option 1.
The sum of the angles of a convex pentagon is:
180 ° * (5 – 2) = 540 °.
By condition, the pentagon is correct, all angles and sides are equal.
Each angle is: 540 ° / 5 = 108 °.
Consider isosceles triangles EAD, BAC.
The angles at the bases of these triangles are:
(180 ° – 108 °) / 2 = 36 °.
Find the degree measure of the DAC angle:
108 ° – 36 ° – 36 ° = 36 °.
Got that:
∠EAD = ∠BAC = ∠DAC = 36 °.
Option 2.
If a circle is described near a regular pentagon, then equal sides – equal chords, will contract equal arcs. The inscribed angles that rest on these arcs are equal.
∠EAD = ∠BAC = ∠DAC.
Q.E.D.