Look at this diagram:DEFGHIJKIf EG and HJ are parallel lines and mHIF= 63°, what is mGFI?°

1. Break Down the Problem

To find $mGFI$, we need to use the information that $EG$ and $HJ$ are parallel lines, and we know the angle $mHIF$.

2. Relevant Concepts

When two parallel lines are cut by a transversal, corresponding angles are equal. In this case, $HIF$ and $GFI$ are formed by the transversal $FI$.

3. Analysis and Detail

• From the problem, $mHIF = 63^\circ$.
• Because angles $HIF$ and $GFI$ are corresponding angles due to the parallel lines $EG$ and $HJ$, we have: $mGFI = mHIF$

4. Verify and Summarize

Since $mHIF = 63^\circ$, we conclude that: $mGFI = 63^\circ$

Final Answer

Thus, $mGFI = 63^\circ$.