Question

With given values of angles, prove that AB || CD
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Answer 1

Answer:

Let the line below CD be EF

First, prove that CD ║ EF

∠DCE + ∠FEC= 150+30

                        =180°

Therefore, CD║ EF-----(1)   (since co-interior angles are supplementary)

Now, prove that AB ║ EF.

              ∠ABE=54°------(2)

             ∠BEF= 24+30=54°----(3)

From (2) and (3) we can say that

            ∠ABE= ∠BEF

Therefore, AB ║ EF----(4)(since alternate interior angles are equal)

Now from (1) and (4) we have,

AB ║ EF

CD ║ EF

So, AB║ CD (If a line is parallel to any 2 lines, then the other two line are parallel)

Hence proved.

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