Answer:
EF ║ CD and AB ║ CD are the parallel segments.
Explanation:
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Since m∠A = m∠D = 42°
Therefore, AB ║ CD and segment AD is the transverse.
Now ∠AEF + ∠IEF = 180° [Supplementary angles]
138° + ∠IEF = 180°
∠IEF = 180 - 138
= 42°
∠IHG + ∠DHG = 180° [ Supplementary angles ]
∠IHG + 122 = 180
∠IHG = 180 - 122
∠IHG = 58°
But ∠IEF ≠ ∠IHG
Therefore, EF and GH are not parallel.
If the segments AB and GH are parallel then ∠IHG = ∠IAB (By the property of alternate angles)
But ∠IHG ≠ ∠IAB
Therefore, AB and GH are not parallel.
Now ∠IEF ≅ ∠IDC ≅ 42° [alternate angles]
which reveals that EF ║ CD
Therefore, EF ║ CD and AB ║ CD.