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

Question 4 Lines And Angles Exercise 7C

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

Question 4 Image - R S Aggarwal Solutions - Mathematics - Class 9 chapter Lines And Angles

Answer:

It is given that AB || CD and BC is a transversal

From the figure we know that ∠BCD and ∠ABC are alternate interior angles

So we get

∠ABC = ∠BCD

In order to find the value of x we can write it as

x + ∠ECD = 70 ……. (1)

It is given that CD || EF and CE is a transversal

From the figure we know that ∠ECD and ∠CEF are consecutive interior angles

So we get

∠ECD + ∠CEF = 180

By substituting the values

∠ECD + 130 = 180

On further calculation we get

∠ECD = 180 - 130

By subtraction

∠ECD = 50

Now by substituting ∠ECD in equation (1) we get

x + ∠ECD = 70

x + 50 = 70

On further calculation we get

x = 70 - 50

By subtraction

x= 20

Therefore, the value of x is 20.

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