Question

Rhombus LMNO has a diagonal line MO, with m<M=747. What is m<LOM?

106
37
53
74

Answer 1

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 \( 360^\circ \):

1. The rhombus has four angles, each pair of opposite angles is equal.
2. 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