Question 276811
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The trick is to realize that the sum of the measures of the interior angles of any  quadrilateral is 360°.  So, if you have two congruent angles that each measure *[tex \Large x]° and two other congruent angles that each measure *[tex \Large y]°, then the following equation must hold:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ 2y\ =\ 360]


But if you divide by 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ y\ = 180]


So now if you extend the sides of your quadrilateral past the vertices, then you can show that you have equal measure opposite interior angles formed by a transversal meaning that you have parallel lines.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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