Question

Rhombus LMNO is shown with its diagonals. Angle MNO measures 112°. What is the measure of angle LMN?

Answer 1

Answer: $68^{\circ}$

Step-by-step explanation:

Since, In the case of rhombus has the congruent pair of opposite angles.

Thus in Rhombus, LMNO, $\angle LMN=\angle LON$

And, $\angle OLM=\angle MNO$

But,  $\angle MNO= 112^{\circ}$

And, $\angle LMN+\angle LON+\angle OLM+\angle MNO=360^{\circ}$

Therefore, $2\angle LMN+112^{\circ}+112^{\circ}=360^{\circ}$

⇒$2\angle LMN=360^{\circ}-224^{\circ}$

⇒$2\angle LMN=360^{\circ}-224^{\circ}$

⇒$\angle LMN=68^{\circ}$

Answer 2

Angle LMN + angle MNO= 180
angle LMN + 112= 180
angle LMN = 180-112
angle LMN = 68°