Question

Question
Rhombus LMNO has a diagonal line MO¯¯¯¯¯¯¯¯¯, with m∠M=74°. What is m∠LOM?(1 point)
Responses which answer is correct and why

106°
106°

53°
53°

74°
74°

37°
37°
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Answer 1

In a rhombus, the diagonals bisect each other at right angles. This means that each diagonal splits the rhombus into two congruent triangles.

Given that \( m\angle M = 74° \), we can analyze the triangle \( LOM \):

- Since the diagonals bisect the angles, \( \angle LOM \) will be half of the angle \( \angle M \).

In a rhombus:

- The diagonals bisect the opposite angles.
- Therefore, \( m\angle LOM = m\angle M = 74° \).

Since \( m\angle M = 74° \) does not directly apply to \( m\angle LOM \) as they are not the same angle but rather related through the diagonals, we need to find \( m\angle LOM \):

- Angles \( M \) and \( O \) are on the same diagonal, and since the diagonals of a rhombus bisect the angles of the rhombus, we have:

\[
m\angle LOM = 180° - m\angle M = 180° - 74° = 106°.
\]

Thus, the correct answer is **106°** because \( m\angle LOM \) is the exterior angle associated with \( m\angle M \) at point L and M in rhombus LMNO.