Wouldn't think so, think of a trapezium shaped like a square with a triangle on one side...
The angles at one end of the figure are both 90o, and the angles at the other end will be supplementary, but not opposite angles.
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No, only in certain, limited circumstances. Eg where a quadrilateral is (can be) circumscribed within a circle.
False. Supplementary angles add to 180degrees.
True
-- Opposite sides are parallel. -- Opposite sides are equal. -- All four sides are equal. -- Adjacent sides are equal. -- Adjacent angles are supplementary. -- Opposite angles are equal. -- Diagonals are perpendicular. -- Interior angles sum to two straight angles. -- Exterior angles sum to two straight angles.
If the lines are perpindicular then each pair of vertical angles are supplementary