Question

quadrilateral vwxy is a kite. what is uy? uy =

Explanation:

Step1: Recall kite - property

In a kite, the diagonals are perpendicular and one diagonal is bisected by the other. Let's assume the diagonals of the kite \(VWXY\) are \(VX\) and \(YW\) which intersect at \(U\). If we assume \(VX\) bisects \(YW\) (a common property of kites), and we know some side - length information. However, since no other information about the relationship between the given side - lengths (\(85\) and \(77\)) and the line segment \(UY\) is provided clearly, if we assume that the given side - lengths are part of right - triangles formed by the diagonals of the kite. Let's assume we can use the Pythagorean theorem. But without more context, if we assume that the given side - lengths are related to the right - triangles formed by the diagonals and one of the right - triangles has hypotenuse \(85\) and one side \(77\).

Step2: Apply Pythagorean theorem

Let the hypotenuse of a right - triangle be \(c = 85\) and one side be \(a = 77\). According to the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(b\) is the other side. So \(b=\sqrt{c^{2}-a^{2}}=\sqrt{85^{2}-77^{2}}=\sqrt{(85 + 77)(85 - 77)}=\sqrt{162\times8}=\sqrt{1296}=36\). If this side \(b\) is equal to \(UY\) (assuming appropriate right - triangle formation within the kite).

Answer:

\(36\)