Question

use the figure below to answer the following question: if ∠lom ≅ ∠nom, which of the following conjectures would be true? om is the angle bisector of m∠nom; m∠lom = m∠nol; m∠lom = m∠nom; om is the angle bisector of m∠lom

Explanation:

1. Recall the definition of congruent angles: If two angles are congruent ($\angle LOM \cong \angle NOM$), their measures are equal, so $m\angle LOM = m\angle NOM$.
2. Analyze other options:

• "OM is the angle bisector of $m\angle NOM$" is incorrect because an angle bisector of $\angle NOM$ would split $\angle NOM$ into two equal parts, but here OM is a side of $\angle NOM$, not a bisector.
• "$m\angle LOM = m\angle NOL$" is incorrect as there's no information to support this equality.
• "OM is the angle bisector of $m\angle LOM$" is incorrect because an angle bisector of $\angle LOM$ would split $\angle LOM$ into two equal parts, but OM is a side of $\angle LOM$, not a bisector.

Answer:

$m\angle LOM = m\angle NOM$