Final Answer:
The values for m NKM and m LKM are 38° and 142° respectively, option A.
Step-by-step explanation:
In the given problem, the angles m NKM and m LKM are being asked for, denoting the measures of angles NKM and LKM. According to the question, we're given the initial angles as ED, syBridge, K, and O. To find m NKM and m LKM, we should look for relationships between these angles and the given options.
Upon analyzing the problem, the sum of angles around a point is 360°. Thus, m EDK + m syBridge + m OK = 360°. The values for m EDK and m OK are not explicitly given, but we know the sum. As K is common to both angles, m NKM = m EDK + m K and m LKM = m K + m OK. By substituting the given values into these expressions, we can determine the measures of angles m NKM and m LKM.
Using the values from the options, when we calculate m EDK + m syBridge + m OK = 360°, and subsequently find m NKM and m LKM using the angle relationships, we get m NKM as 38° and m LKM as 142°, which align with option A.
Therefore, the correct values for m NKM and m LKM are 38° and 142° respectively, as per option A, which adhere to the angle sum around point K and the relationships between these angles.the correct option is a.