Final answer:
The measure of angle MLN is calculated by subtracting the sum of the given angles OLN and MLO from 180 degrees, which gives us 97 degrees.
Step-by-step explanation:
To find the measure of angle MLN, we need to know that the sum of the angles in a triangle equals 180 degrees. We are given m∠OLN = 31° and m∠MLO = 52°. These two angles are adjacent to angle MLN, forming a triangle. Therefore, to find m∠MLN, we subtract the sum of m∠OLN and m∠MLO from 180°:
- m∠MLN = 180° - (m∠OLN + m∠MLO)
- m∠MLN = 180° - (31° + 52°)
- m∠MLN = 180° - 83°
- m∠MLN = 97°
The correct answer is 97° which isn't provided in the multiple choices. It seems there might be a mistake either in the provided choices or in the question itself.