In parallelogram PQRS, angle P=32 degree, angle Q=147 degree, angle R=30 degree, angle S=151 degree, side PQ=5.5 cm, QR=3.8 cm, RS=6.0 cm, PS=3.1 cm, the lengths of the sides of the image quadrilateral TUVW are TU = 5.5 cm, UV = 6.0 cm, and VW = 6.93 cm.
The given question is related to the transformation of parallelogram PQRS into the image TUVW. To find the lengths of the sides of the image quadrilateral, we can use the properties of parallelograms and the given information.
Using the fact that opposite angles in a parallelogram are congruent, we can determine that angle U = angle Q = 147 degrees and angle W = angle S = 151 degrees.
The sum of the angles in a quadrilateral is 360 degrees, so angle T = 360 - angle U - angle W = 360 - 147 - 151 = 62 degrees.
Since opposite sides of a parallelogram are congruent, we can determine that TU = PQ = 5.5 cm and UV = RS = 6.0 cm.
By using the given side lengths, we can find the length of VW.
Since the opposite sides of a parallelogram are parallel, we can use the fact that corresponding angles are congruent to find angle PQR = angle SRQ = 32 degrees.
Then, we can use the Law of Cosines to find the length of side VW: VW =
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