Question

rhombus lmno is shown with its diagonals. angle mno measures 112°. what is the measure of angle lmn? 34° 45° 56° 68°

Explanation:

Step1: Recall properties of a rhombus

In a rhombus, adjacent angles are supplementary, meaning their sum is \(180^\circ\). So, \(\angle MNO\) and \(\angle LMN\) are adjacent angles in rhombus \(LMNO\).

Step2: Calculate \(\angle LMN\)

Let \(\angle LMN = x\). We know that \(\angle MNO = 112^\circ\) and \(x + 112^\circ= 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 112^\circ\).
\(x = 68^\circ\)

Answer:

\(68^\circ\) (corresponding to the option with \(68^\circ\))