how can example 2 be right because 110+50 =160 and the alternate interior angles are not equal

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See, we are not at all taking 1100 into consideration. We are taking AB to be transversal for PQ and RS. In that case, L UXY + L XYV = 180[ since 130 +50 = 180] Using the converse of the theorem "Co-interior angles are supplimentary", we can say that PQ and RS are parallel with transversal AB

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CD AND AD ARE TRANSVERSAL AND UX IS NOT A TRANSVERSAL

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the measure taken are of angles lieing on the same side of the parallel lines not on transversal 

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