 # RS Aggarwal Solutions Class 9 Mathematics Solutions for Lines And Angles Exercise 7C in Chapter 7 - Lines And Angles

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