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: Use the property of adjacent angles in a rhombus

In a rhombus, adjacent angles are supplementary. That is, if two adjacent angles are \( \angle MNO\) and \( \angle LMN\), then \( \angle MNO+\angle LMN = 180^{\circ}\)

Step2: Solve for \( \angle LMN\)

Given \( \angle MNO = 112^{\circ}\). Substitute into the formula:
\(\angle LMN=180^{\circ}-\angle MNO\)
\(\angle LMN = 180^{\circ}- 112^{\circ}\)
\(\angle LMN=68^{\circ}\)

Answer:

\(68^{\circ}\) (the fourth option)