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Mathematical proof of constructing eight-character congruence in the second day of junior high school
As shown in figure 1, line AB and CD intersect at point O, connecting AD and CB. We call the figure with the shape of 1 the "8" shape. As shown in Figure 2, under the condition of Figure 1, the bisectors AP and CP of ∠DAB and ∠BCD intersect at point P and CD and CB.

(1) In the figure 1, please directly write the quantitative relationship between ∠A, ∠B, ∠C and ∠D:?

(2) Look carefully, the number "8" in Figure 2:? Answer?

(3) In Figure 2, if ∠ d = 40 b = 36, try to find ∠P times;

(4) If ∠D and ∠B are arbitrary angles in Figure 2, and other conditions remain unchanged, what is the quantitative relationship between ∠P and ∠D and ∠B? (Just write a conclusion directly)

Solution: (1) Conclusion: ∠ A+∠ D = ∠ C+∠ B;

(2) Conclusion: 6;

(3) by ∠ d+∠1+∠ 2 = ∠ b+∠ 3+∠ 4 ① (∠ aod = ∠ cob),

By ∠ 1=∠2, ∠3=∠4,

∴40 +2∠ 1=36 +2∠3

∴∠3-∠ 1=2 ( 1)

By ∠ONC=∠B+∠4=∠P+∠2,②

∴∠p=∠b+∠4-∠2=36+2 = 38;

(4) From ①∠D+2∠ 1=∠B+2∠3,

From ②2∠B+2∠3=2∠P+2∠ 1

①+②De:∠D+2∠B+2∠ 1+2∠3 =∠B+2∠3+2∠P+2∠ 1。

∠D+2∠B=2∠P+∠B。

∴∠P= half (≈d+≈b)