Question
Look at this diagram:
D
E
F
G
H
I
J
K
If
EG
and
HJ
are parallel lines and mHIF= 63°, what is mGFI?
D
E
F
G
H
I
J
K
If
EG
and
HJ
are parallel lines and mHIF= 63°, what is mGFI?
Answers
GPT-4o mini
To solve for \( mGFI \), we first need to analyze the diagram and the information given:
1. We know that lines \( EG \) and \( HJ \) are parallel.
2. The measure of angle \( mHIF \) is given as \( 63^\circ \).
Since \( EG \) and \( HJ \) are parallel lines, we can apply the concept of alternate interior angles. The angle \( HIF \) would be an alternate interior angle to angle \( GFI \).
From the properties of parallel lines, we find that:
\[
mHIF = mGFI
\]
Thus:
\[
mGFI = mHIF = 63^\circ
\]
Therefore, the measure of angle \( GFI \) is \( \boxed{63^\circ} \).
1. We know that lines \( EG \) and \( HJ \) are parallel.
2. The measure of angle \( mHIF \) is given as \( 63^\circ \).
Since \( EG \) and \( HJ \) are parallel lines, we can apply the concept of alternate interior angles. The angle \( HIF \) would be an alternate interior angle to angle \( GFI \).
From the properties of parallel lines, we find that:
\[
mHIF = mGFI
\]
Thus:
\[
mGFI = mHIF = 63^\circ
\]
Therefore, the measure of angle \( GFI \) is \( \boxed{63^\circ} \).