Question

Rhombus LMNO has a diagonal line LN, and MNL is 55 degrees. What is angle N?

Answer 1

In a rhombus, the diagonals bisect each other at right angles. Since you have rhombus \(LMNO\) with diagonal \(LN\), and angle \(MNL\) is \(55^\circ\), we can find angle \(N\) using the properties of the rhombus.

First, note that:
- \(MNL\) is one of the angles formed by the intersection of diagonal \(LN\) with side \(LM\).

Since diagonals bisect the angles of the rhombus:
- Triangle \(MNL\) is formed, and angles \(MNL\) and \(NLM\) are adjacent angles:
- Therefore, \(NLM = 55^\circ\) as well.

Now, in triangle \(MNL\):
- The angle sum property of a triangle states that the sum of the angles is \(180^\circ\):
\[
\angle MNL + \angle NLM + \angle LMN = 180^\circ
\]
Substituting the known angles:
\[
55^\circ + 55^\circ + \angle LMN = 180^\circ
\]
\[
110^\circ + \angle LMN = 180^\circ
\]
\[
\angle LMN = 180^\circ - 110^\circ = 70^\circ
\]

Now, since in rhombus \(LMNO\), opposite angles are equal:
- Angle \(N\) (which is the same as angle \(LMN\)) is \(70^\circ\).

Thus, the measure of angle \(N\) is \(70^\circ\).