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PLEASE HELP! WILL GIVE BRAINLIEST!!
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.

PLEASE HELP WILL GIVE BRAINLIESTWhich angle determines whether or not quadrilateral SVUT is a trapezoidWhat measure would the angle need to be for SVUT to be a class=

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Answer:  The answer is ∠TUV must be 68°.

Step-by-step explanation:  We are given a quadrilateral SVUT, with ∠SUV = 112°. We are to find the angle which determines whether or not the quadrilateral SVUT is a trapezoid and what will be the measure of thet particular angle.

We know that for a quadrilateral to ba a trapezoid, we need a pair of opposite sides parallel.

In SVUT, the sides UV and ST cannot be parallel as shown in the figure. So, the only choice is SV must be parallel to UT.

For that, we need

∠TUV + ∠SUV = 180°, because the sum of interior angles must be equal to two right angles.

This implies that

∠TUV = 180° - °112 = 68°.

Thus, ∠TUV determines whether or not SVUT is a trapezoid, and for being a trapezoid the measure of angle TUV must be 68°.

Answer:

∠TUV  is the angle which determines whether or not quadrilateral SVUT is a trapezoid and

Measure of ∠TUV is 68° is needed to be for SVUT to be a trapezoid.

Step-by-step explanation:

Given the figure SVUT in which ∠V=112°. we have to tell the angle which determines whether  or not quadrilateral SVUT is a trapezoid.

As we know one pair of opposite sides of trapezium is parallel

∴ ∠SVU and ∠TUV and also  ∠VST and ∠UTS are co-interior angles hence are supplementary.

As ∠SVU is given ∴ ∠TUV  is the angle which determines whether or not quadrilateral SVUT is a trapezoid.

Now, we have to tell the measure of angle

If measure of ∠TUV is such that the sum of ∠SVU and ∠TUV is 180° then quadrilateral SVUT is a trapezoid.

⇒ ∠SVU +∠TUV = 180°     ( ∵ Co-interior angles)

⇒ 112° + ∠TUV = 180°

⇒  ∠TUV =180-112=68°

hence, measure of ∠TUV is 68° is needed to be for SVUT to be a trapezoid.

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