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Question

In the figure, if AB ∥ CD, CD ∥ EF and y:z=3:7, then the value of x is:

A
112
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B
116
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C
96
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D
126
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Solution

The correct option is D 126
Given, CD || EF
CGH=FHG [Alternate interior angles]
CGH=z

Also,
CGI+CGH=180 [Linear pair]
y+z=180

Given: y:z=3:7
Let y=3k and z=7k for some k ϵ R
then, y+z=180
3k+7k=180
10k=180
k=18

z=7k=7(18)=126

Also, AB || CD
x=CGH [Corresponding angles]
x=126

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