So,
Given RK=5, RY=13 and the measure of angle YRZ=67, we're going to find the measure of KY.
Notice the following:
The diagonals of a rhombus cut and form a perpendicular segment. Thus, we obtain the following right triangle:
To find KY, we could use the pythagorean theorem:
![\begin{gathered} KY^2=13^2-5^2 \\ KY=\sqrt[]{169-25} \\ KY=\sqrt[]{144} \\ KY=12 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/z0npve3zarv4s5yxwz0b76bam8ln0ably1.png)
Therefore, KY=12.