The textbook says that ∠2 and ∠4 are the complementary angles of ∠3.

And ∠ 2+∠ 3 = 180 is a graphic property, not a known condition.

So ∠2 and ∠4 are adjacent complementary angles of ∠3,

So from ∠ 2+∠ 3 = 180, we can also get ∠ 4+∠ 3 = 180.

Your thinking is very correct.

However, the following steps are not appropriate.

∠ 1=∠4 is not a known condition, but is obtained from∠1= ∠ 2 and ∠2=∠4.

So the correct step is:

Solution: ∫≈ 1 =∠2, ∠2=∠4,

∴∠ 1=∠4,

∵∠3+∠4= 180 ,

∴∠ 1+∠3= 180 。