Final answer:
To find mZ52 in a quadrilateral with parallel sides where MZ2 is 27°, use the properties of a parallelogram to determine that mZ52 is the supplementary angle to MZ2, which calculates to 153°.
Step-by-step explanation:
The original question contains some irrelevant information and typographical errors that do not pertain to the problem of calculating an angle in a quadrilateral. To find the measure of angle Z52 in quadrilateral ABCD where AB is parallel to CD and MZ2 is given as 27°, we need to use the fact that opposite angles in a parallelogram are equal and the sum of adjacent angles is 180° due to the parallel sides.
Since MZ2 is 27° and AB is parallel to CD, by properties of parallel lines and the fact that ABCD is a parallelogram (implied by one pair of opposite sides being parallel), we know that the angle opposite to MZ2 will also be 27°. Therefore, mZ52 will be the supplementary angle to 27°. Thus, mZ52 = 180° - 27° = 153°.
There seems to be a typographical error in the options provided as none of them match the calculated value. None of the SEO keywords provided are relevant to the problem at hand.