Question

Which angle determines whether or not quadrilateral SVUT is a trapezoid? What measure would the angle need to be for SVUT to be a trapezoid? Provide theorems and postulates you used and explain your reasoning.

Answer 1

Answer: The answer is ∠TUV.

Step-by-step explanation: Given in the question a quadrilateral SVUT with ∠SVU = 112°. We need to determine the angle whose measure will decide whether or not the quadrilateral SVUT is a trapezoid.

We know that for a quadrilateral to be a trapezoid, we need only one condition that one pair of opposite sides must be parallel.

So, in quadrilateral SVUT, since the measure of ∠SVU is given, so we can decide it is a trapezoid or not if we know the measure of ∠TUV. As ST and UV cannot be parallel, so its meaningless to determine ∠TSV.

For SV and TU to be parallel to each other, we need

∠SVU + ∠TUV = 180° (sum of interior alternate angles).

Therefore,

∠TUV = 180° - 112° = 68°.

Thus, we need to determine ∠TUV and its measure shoul be 68°.