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In the given figure, AB || CD. Find the value of x.

Answer:

Parallel lines are defined as two or more lines that lie in the same plane but never intersect. They are equidistant from one another and possess the same slope.

Draw a line through point C and name it as FG where FG || AE

We know that CG || BE and CE is a transversal

From the figure we know that ∠GCE and ∠CEA are alternate angles

So we get

∠GCE = ∠CEA = 20

It can also be written as

∠DCG = ∠DCE - ∠GCE

By substituting the values we get

∠DCG = 130 - 20

By subtraction we get

∠DCG = 110

We also know that AB || CD and FG is a transversal

From the figure, we know that ∠BFC and ∠DCG are corresponding angles

So we get

∠BFC = ∠DCG = 110

We know that FG || AE and AF is a transversal

From the figure, we know that ∠BFG and ∠FAE are corresponding angles

So we get

∠BFG = ∠FAE = 110

∠FAE = x = 110

Therefore, the value of x is 110.

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