Chapter 5, Problem 27CUR

To determine

To Complete: the statement $\angle LOM\cong ?\cong ?\cong ?$ in a rhombus $LMNO$ shown in figure.

Answer to Problem 27CUR

  $\angle NOM,\angle OMN\text{ and }\angle LMO$

Explanation of Solution

Given Figure is shown as.

  

  $LMNO$ is a rhombus.

Calculation:

Since, $LMNO$ is a rhombus therefore $LM$ is parallel to $ON$ .

When two parallel lines are cut by a transversal then alternate angles are equal therefore.

  $\angle LOM\cong \angle OMN$ .

In $\Delta LOM$ .

Since, $LM\cong OL$ therefore using angle opposite to these sides will be equal.

  $\angle LOM\cong \angle LMO$ .

Similarly,

In $\Delta LOM$ , $MN\cong ON$

  $\angle OMN\cong \angle NOM$

Therefore, the answer is $\angle NOM,\angle OMN\text{ and }\angle LMO$