Page 6 - Ans Sub

So, it can be written as
0
∠BCD + ∠EDC = 180
0
0
∠BCD + 75 = 180
0
0
∠BCD = 180 – 75
0
∠BCD = 105
From the figure, we know that ∠BCD and ∠ABC are vertically opposite angles
So, we get
0
∠BCD = ∠ABC = x = 105
0
∠ABC = x = 105
0
Therefore, the value of x is 105 .
8. In the figure, AB || CD || EF. Find the value of ‘x’ .
Solution:

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
0
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
0
∠ECD + ∠CEF = 180
0
0
∠ECD + 130 = 180
0
0
∠ECD = 180 - 130
0
∠ECD = 50
Now by substituting ∠ECD in equation (1) we get
0
x + ∠ECD = 70
0
0
x + 50 = 70
0
0
x = 70 - 50
0
x = 20
0
Therefore, the value of x is 20 .

6