1. (Method 1) It is proved that the vertex E of ∠2 makes the straight line EF parallel to the straight line AB.

Because EF// AB, ∞∠AEF =∠ 1 = 50 (internal dislocation angles are equal).

So ∠ FEC = ∠ 2-∠ AEC = 80-50 = 30.

Because ∠ FEC = ∠ 3 = 30, EF // BC, AB // EF // CD.

(Method 2) Proof: Let the vertex of ∠2 be E and connected with AC.

Because ∠ 2 = 80, ∠ EAC+∠ ECA =180-∠ 2 =180-80 =100.

so∠ 1+∠EAC+∠ECA+∠3 = 50+ 100+30 = 180。

So AB // CD (internal angles are complementary and two straight lines are parallel)

2. proof: EF // AB.

Therefore, ∞∠EAB+∠AEF = 180 (complementary angle) (1).

Because ∠ e+∠ Abe+∠ CDE = 360 (known) (2)

(2)-( 1) Therefore, ∞∠FED+∠D = 180.

So AB // CD (internal angles are complementary and two straight lines are parallel)

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