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 ${180}^{\circ }$: $$\mathrm{\angle }MNL+\mathrm{\angle }NLM+\mathrm{\angle }LMN={180}^{\circ }$$ Substituting the known angles: $${55}^{\circ }+{55}^{\circ }+\mathrm{\angle }LMN={180}^{\circ }$$ $${110}^{\circ }+\mathrm{\angle }LMN={180}^{\circ }$$ $$\mathrm{\angle }LMN={180}^{\circ }-{110}^{\circ }={70}^{\circ }$$

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 ${70}^{\circ }$.