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In cyclic quadrilateral ABED,
∠DAB +∠BED = 180°
(Opposite angles of a cyclic quadrilateral are supplementary)
∠BED = 180° - ∠DAB --Eq.1
Now again in cyclic quad. BCFE
∠BEF + ∠BCF = 180° ∠BEF = 180° -∠BCF --Eq.2

∠BED +∠BEF = 180°(Linear pair)
Using Eq.1 and Eq.2 we can rewrite it as ,
180°- ∠DAB +180° -∠BCF = 180°
After solving,
∠DAB +∠BCF = 180°

But, they are interior angles on the same side of transversal.Interior angles on the same side of transversal are supplementary only if the lines are parallel.

Therefore, ABC || DEF
1 5 1
Perfect solution full mark excellent presentation
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