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

Answer 1

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

Given that \( \angle MNL = 55^\circ \), we recognize that:

1. The diagonals LN and MO intersect at point P, creating \( \angle MNL \) and \( \angle MNP \) as parts of \( \angle MNO \).
2. Because diagonals bisect the angles, \( \angle MNL = \angle MNP = 55^\circ \).

To find \( \angle MNO \), we use the fact that the two angles \( \angle MNL \) and \( \angle MNO \) form a linear pair and must sum to \( 180^\circ \). This gives us:

\[ \angle MNO = 180^\circ - \angle MNL - \angle MNP = 180^\circ - 55^\circ - 55^\circ = 180^\circ - 110^\circ = 70^\circ. \]

Therefore, the measure of angle \( \angle MNO \) is:

\[ m<MNO = 70^\circ. \]