If FH and IK are parallel lines and mIJL = 46°, what is mFGE?

Answer 1

To find the measure of angle \( mFGE \), we first need to analyze the relationship between the angles given the information: lines \( FH \) and \( IK \) are parallel and \( mIJL = 46^\circ \).

Since \( FH \) and \( IK \) are parallel lines, any transversal that crosses these lines creates corresponding angles, alternate interior angles, and other angle relationships.

Without knowing the exact layout of the angles or the transversal involved, we can implement a general approach:

1. Identify the transversal: If \( IJ \) serves as a transversal between the two parallel lines \( FH \) and \( IK \) and it creates the angle \( IJL \), then \( mFGE \) could relate to \( mIJL \) depending on the specific relationships.

2. Identify the angle relationships:

   • If \( IJL \) and \( FGE \) are corresponding angles, they will be equal, in which case \( mFGE = 46^\circ \).
   • If \( IJL \) and \( FGE \) are alternate interior angles, they will also be equal, and thus \( mFGE = 46^\circ \).

Without exact information on how \( FGE \) is positioned relative to \( IJL \), assuming these angles are corresponding or alternate would imply:

\[ \text{If } FGE \text{ is corresponding or alternate to } IJL: \quad mFGE = 46^\circ \]

Thus, based on this reasoning, if \( FGE \) is appropriately positioned in relation to the parallel lines, then:

\[ mFGE = 46^\circ \]