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Question

# Can you draw two quadrilaterals each having two $130^{\circ}$ angles and two $50^{\circ}$ angles that are not similar? Justify your answer.

Solution

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Quadrilateral 1: $50\text{\textdegree},50\text{\textdegree}, 130\text{\textdegree}, 130\text{\textdegree}$ (an isosceles trapezoid)

Quadrilateral 2: $50\text{\textdegree},130\text{\textdegree}, 50\text{\textdegree}, 130\text{\textdegree}$ (a parallelogram)

In order for the two quadrilaterals not to be similar when their angles have the same measures we should be able to draw them so that the angles should be placed in different order.

For example:

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