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 the property of a rhombus

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

Step2: Solve for \(\angle LMN\)

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

Answer:

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