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 angles at each vertex.

Given that \( \angle MNL = 55^\circ \), this angle is split into two equal angles by diagonal \( LN \). Therefore, we can find \( \angle NML \):

\[ \angle NML = \angle MNL = 55^\circ \]

Now, since \( \angle MNL \) and \( \angle NML \) are angles associated with vertex \( N \), the remaining angle \( \angle N \) (the angles at vertex \( N \) split by the diagonal) will be:

\[ \angle N = \angle MNL + \angle NML = 55^\circ + 55^\circ = 110^\circ \]

Since the diagonals of a rhombus bisect the angles, both angles \( MNO \) and \( NMO \) must be equal to \( \angle N \) but on the opposite side, and so:

\[ \angle MNO = \angle MNL = 55^\circ \]

Thus,

\[ m\angle MNO = 55^\circ \]