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Answer: Since <HGI and <HIG are congruent then <HGI must be 65. This is because <HIG is supplementary to <DIG which is 115, and the supplementary angle to 115 is 65. Since <EGB is 50 and <HGI is 65, <BGI is 180-115=65, once again because the angles must add up to 180. on a straight line. Since BGI and DIG are supplementary (115+65=180), they are consecutive interior angles and thus AB and CD must be parallel lines, or else it is not possible.

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