Question

In the fig, ray AB || ray CD. From the information given in the figure, find the value of x​

Answer 1

Let AB is parallel to FG, then ∠ABE=∠BEG=120°(Alternate angles)

Also, it is given that CD is parallel to AB and we have assumed that AB is parallel to FG, then CD is parallel to FG

Therefore, considering CD║FG and CE is the transversal, then

∠DCE+∠CEG=180°(Co-interior angles)

100°+∠CEG=180°

∠CEG=80°

Now, ∠BEG=∠BEC+∠CEG

120°=x+80°

x=40°

Thus, the value of the ∠BEC=x=40°

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Step-by-step explanation:

Answer 2

Answer:

40°

Step-by-step explanation:

Extend AB to intercept CE at a point F

Now EBF forms a triangle (Refer the image)

∠EBF = 180 -120 =60° (AS a straight line is 180°)

∠BFC = ∠ECD = 100° (AB║CD alternate interior angles)

∠BFE =180 - ∠BFC =180 - 100 =80°  (AS a straight line is 180°)

∠BEF = 180-(∠EBF+∠EFB) =180-(60+80) =180-140 =40°