Rhombus LMNO has a diagonal line LN¯¯¯¯¯¯¯¯, and ∠MNL is 55 degrees. What is m∠MNO?(1 point)

m∠N=
°

1 answer

In a rhombus, the diagonals bisect each other at right angles and also bisect the vertex angles. Given the rhombus LMNO and the information that ∠MNL = 55 degrees, we can derive the measures of the other angles.

Since the diagonals bisect the angles, we know that:

\[ m\angle MNL = m\angle NMO = 55^\circ \]

This means:

\[ m\angle MNO = 180^\circ - (m\angle MNL + m\angle NMO) \]

Substituting the known values:

\[ m\angle MNO = 180^\circ - (55^\circ + 55^\circ) \] \[ m\angle MNO = 180^\circ - 110^\circ \] \[ m\angle MNO = 70^\circ \]

Thus,

\[ m\angle MNO = 70^\circ \]