prove that ab II cd.
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angle1 = 55
angle BMN = angle2 + angle3
= 20 + 35
= 55
therefore angle1 = angle BMN
we can say that AB II MN (alternate interior angles)
angle3 + angle4 = 35 + 145
= 180
we can say that MN II CD (cointerior angles are supplementary)
now AB II MN II CD
therefore AB II CD
angle BMN = angle2 + angle3
= 20 + 35
= 55
therefore angle1 = angle BMN
we can say that AB II MN (alternate interior angles)
angle3 + angle4 = 35 + 145
= 180
we can say that MN II CD (cointerior angles are supplementary)
now AB II MN II CD
therefore AB II CD
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