Solution: If this question is answered as quickly as possible, the answer is 30 days. I have done several problems of this kind. For example, see the figure below, where 1 is the subject; Figure 2 is the deformation problem I have done, which is figure 1. The analysis of the answer to this question is mainly based on the proposition I.7 in Geometry, which reads: "When two line segments intersect at both ends of a line segment, it is impossible to have two line segments at another point on the same side, which are equal to the first two line segments, that is, the two line segments from each intersection point to the same end point are equal." The last sentence, there is no loophole to drill; In fact, it is the uniqueness theorem of points.

For our problem, we notice that in △ABC, ∠A=40D= (even number) 4 *10d; ∠B =∠C = 70D； The sum of the internal angles of △ABC is 180D.

As far as AD is concerned, it is a line drawn from ∠A, and the intersection point of 20 degrees and 40 degrees is the vertex of the base angle respectively; Obviously: ∠ BDC =120d; Is even12 *10; So ∠BAD must be 10n(n∈N*). Some people may say, if it's 5D, can't it? If it is 5 degrees, then ∠BDC= odd number * 10, then the angle of 5 degrees can be hidden in △DBC. If it is a mantissa other than 5 and n* 10, then the two base angles can't be the same degree of ni and j* 10 (the subscripts I and j of n indicate that the degrees of the two angles are different). This theory is both a point uniqueness theory and an angle incompatibility theory-my personal use does not belong to the official forum.

Based on the above analysis, introduce auxiliary lines, let AH⊥BC be in H, and extend CD to AB be in E, then CE⊥AB, DJ⊥AH, ED=DJ (according to the theory of angular incompatibility).

So AD is the bisector of ∠BAH angle (the points with equal distance on both sides of the angle are on the bisector of the angle); Because ∠BAH=20D, the angle divided into two n* 10D can only be10d+10d; That is, ∠ bad = ∠ dah =10d; ∠ DAC = ∠ BAC-∠ Bad = 40d-10d = 30d. Complete the solution.

There are also some auxiliary lines in the figure to analyze the equivalence relationship of solving problems; For reference.