Question

Rhombus LMNO has a diagonal line MO¯¯¯¯¯¯¯¯¯ , with m∠M=74° . What is m∠LOM ?(1 point) Responses 37° 37° 74° 74° 53° 53° 106°

Answer 1

In a rhombus, the diagonals bisect each other at right angles and they also bisect the angles of the rhombus.

Given that \( m\angle M = 74° \), we can find \( m\angle L \) because in a rhombus, opposite angles are equal and adjacent angles are supplementary.

So, \( m\angle L = 74° \) (opposite angle)

Now, since adjacent angles are supplementary:

\[
m\angle M + m\angle L = 180°
\]

\[
74° + m\angle L = 180°
\]

This means:

\[
m\angle L = 180° - 74° = 106°
\]

Now, the diagonals bisect the angles, so \( \angle LOM \) is half of \( \angle L \):

\[
m\angle LOM = \frac{m\angle L}{2} = \frac{106°}{2} = 53°
\]

Therefore, the measure of \( m\angle LOM \) is **53°**.