In a rhombus, the diagonals bisect the angles at the vertices. Since you are given that \(\angle MNL\) is 55 degrees, we can use this information to find the other angles.
- In a rhombus, \(\angle MNL\) and \(\angle MNO\) share the diagonal \(LN\). This means that \(\angle MNL\) and \(\angle MNO\) are congruent: \[ m\angle MNL = m\angle MNO \] Therefore: \[ m\angle MNO = 55^\circ \]
However, it's important to note that since \(MN\) is also part of a straight line with \(MO\) in the rhombus, we may need to find the relationship considering the properties of rhombus.
- Recall that the opposite angles in a rhombus are equal and that adjacent angles are supplementary: \[ m\angle MNL + m\angle MNO = 180^\circ \] Given \(m\angle MNL = 55^\circ\): \[ 55^\circ + m\angle MNO = 180^\circ \] Thus: \[ m\angle MNO = 180^\circ - 55^\circ = 125^\circ \]
So the measure of angle \(MNO\) is \(125^\circ\).