Question
If DF and GI are parallel lines and mFEH = 42°, what is mIHE?
Answers
GPT-4o mini
To solve for \( mIHE \) given that lines \( DF \) and \( GI \) are parallel and \( mFEH = 42^\circ \), we can use the properties of angles formed by parallel lines and a transversal.
Assuming that \( FE \) serves as a transversal intersecting the parallel lines \( DF \) and \( GI \), the angle \( FEH \) and angle \( IHE \) are alternate interior angles. By the properties of parallel lines, alternate interior angles are congruent, meaning:
\[
mIHE = mFEH
\]
Since \( mFEH = 42^\circ \), we conclude that:
\[
mIHE = 42^\circ
\]
So, the value of \( mIHE \) is \( 42^\circ \).
Assuming that \( FE \) serves as a transversal intersecting the parallel lines \( DF \) and \( GI \), the angle \( FEH \) and angle \( IHE \) are alternate interior angles. By the properties of parallel lines, alternate interior angles are congruent, meaning:
\[
mIHE = mFEH
\]
Since \( mFEH = 42^\circ \), we conclude that:
\[
mIHE = 42^\circ
\]
So, the value of \( mIHE \) is \( 42^\circ \).
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