Question

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

106°
106°

53°
53°

74°
74°

37°
37°
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Answer 1

In a rhombus, opposite angles are equal, and the opposite angles are bisected by the diagonals. Given that \( m\angle M = 74^\circ \), we know that \( m\angle O = 74^\circ \) as well because they are opposite angles in the rhombus.

Since the diagonals bisect the angles, \( m\angle LOM \) and \( m\angle MON \) together make up angle \( m\angle M \). Thus, we know:

\[
m\angle LOM + m\angle MON = 74^\circ
\]

But also, \( m\angle LOM = m\angle MON \) because the diagonals bisect the angles. Therefore, let \( m\angle LOM = x \).

So we have:

\[
x + x = 74^\circ \quad \Rightarrow \quad 2x = 74^\circ \quad \Rightarrow \quad x = 37^\circ
\]

Thus,

\[
m\angle LOM = 37^\circ
\]

The correct answer is \( \boxed{37^\circ} \).