In a rhombus, the diagonals bisect each other at right angles. Therefore, in rhombus LMNO, diagonal MO bisects angle L and angle N.
Given that \( m\angle M = 747^\circ \), this is not a typical angle measure as angles in a geometric figure cannot exceed \( 360^\circ \). It seems either there is a mistake in the provided information, or you meant the measure of angle \( M \) to be something else.
Assuming you were looking for the measure of \( m\angle LOM \), and you may have intended to provide an angle measure less than \( 360^\circ \):
- The rhombus has four angles, each pair of opposite angles is equal.
- Since diagonals of a rhombus bisect the angles at the vertices, we know:
\[ m\angle LOM + m\angle M = 180^\circ \]
Since \( \angle M \) should refer to the angle adjacent to \( L \) around point O (which is divided by the diagonal):
- If \( m\angle M = 74^\circ \) (as a guess based on your options), then half of angle \( M \) (which is part of angle \( LOM \)) can be calculated with:
\[ m\angle LOM = m\angle M \div 2 \] \[ m\angle LOM = 74^\circ \div 2 = 37^\circ \]
Thus, assuming \( m\angle M = 74^\circ \), then:
\[ m\angle LOM = 37^\circ \]
This leads to the answer being \( 37^\circ \).
If \( m\angle M \) was originally given as \( 74^\circ \), \( m\angle LOM \) is \( 37^\circ \).
Now, confirming it within the options presented, the measure of \( m\angle LOM\) is \( 37\).
Answer:
37