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Question 1069811: Always, sometimes, or never? All consecutive angles in a quadrilateral are supplementary.
Found 2 solutions by Boreal, KMST:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Sometimes.
If it is a square or a parallelogram, it would be.
If a trapezoid it would not be.
All angles add to 360 degrees but consecutive ones may or may not be supplementary.
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Sometimes.
Consecutive angles in a parallelogram are supplementary,
but in other quadrilateral it is no so.
If two consecutive angles are supplementary,
they must be "sandwiched" between parallel lines,
and if consecutive angles are between parallel lines,
they are supplementary.
The parallel lines containing the parallel sides,
and the line containing the in-between side
form 8 angles.
From those 8, two are consecutive angles of the quadrilateral.
Each of those angles has a congruent alternate interior angle
at the next vertex that is adjacent and supplementary
to the other angle of the quadrilateral.
So, if all pairs of consecutive angles in a quadrilatetal are supplementary,
the quadrilateral is a parallelogram
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