Solve a summer homework math problem 7th grade .

1）。United AdBecause of CD AF, the angle CDA = angle DAF (inner wrong angle) because of the angle CDE = angle BAF

Therefore angle eda = angle dab

Hence de ab (inner wrong angle).

2）。In quadrilateral ABCD and quadrilateral ADEF.

Angular CDA + Angular DAB = Angular EDA + Angular DAF

Therefore the angle c + angle b = angle e + angle f

Therefore: 124 + 90 ° = 80 ° + angle f

Angle f = 134°

Solution: Connect AD, 1) Because: CD AF

So daf= cda

And because, cde= baf

So bad= ade

So ab de (the inner wrong angles are equal).

2) Since: the sum of the inner angles of the quadrilateral is equal, so: the sum of the internal angles of the quadrilateral abcdd = the sum of the internal angles of the quadrilateral adef.

cda+ ∠c+∠b+∠bad=∠ade+∠f+∠e +∠dafc+∠b=∠f+∠e

124+90=80+∠f

f = 134 degrees.

1)ab//de

Proof: Extend DE to point G, because Cd AF so DGA+ CDE=180 degrees.

And because, cde= baf

So BAF+ DGA=180

Therefore, AB de (complementary to the internal angles of the same side, two straight lines parallel) prolongs the intersection of CB at the point H

Because of ab bc

So hba=90

Because c=124°

So bha=180-124=56

So bah=180-56-90=34

So baf=180-34=146

So f=720-146*2-90-124-80=134

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