To find the arc measure of arc MN in triangle LMN inscribed in a circle with diameter LM and the inscribed angle N at vertex N, we can use the properties of inscribed angles.
The inscribed angle N (which is 37°) subtends arc MN. The measure of the arc that is subtended by an inscribed angle is twice the measure of the angle itself.
So, the arc measure of MN can be calculated as follows:
\[ \text{Arc measure of } MN = 2 \times \text{Angle N} = 2 \times 37° = 74° \]
Thus, the arc measure of MN is 74°.