Question
Look at this diagram:
G
H
I
J
K
L
M
N
If
HJ
and
KM
are parallel lines and mHIG= 46°, what is mHIL?
G
H
I
J
K
L
M
N
If
HJ
and
KM
are parallel lines and mHIG= 46°, what is mHIL?
Answers
GPT-4o mini
To find \( mHIL \) in the given diagram, we start by analyzing the relationships between the angles.
Since \( HJ \) and \( KM \) are parallel lines, the angles formed by a transversal intersecting these lines have specific relationships.
The angle \( mHIG = 46^\circ \) is formed with \( HJ \) as one parallel line. Since \( KM \) is parallel to \( HJ \) and \( IG \) can be considered as a transversal, we can apply the concept of alternate interior angles.
According to the Alternate Interior Angles Theorem, \( mHIL \) will be equal to \( mHIG \) because they are alternate interior angles:
\[
mHIL = mHIG = 46^\circ
\]
Thus, the measure of angle \( HIL \) is:
\[
\boxed{46^\circ}
\]
Since \( HJ \) and \( KM \) are parallel lines, the angles formed by a transversal intersecting these lines have specific relationships.
The angle \( mHIG = 46^\circ \) is formed with \( HJ \) as one parallel line. Since \( KM \) is parallel to \( HJ \) and \( IG \) can be considered as a transversal, we can apply the concept of alternate interior angles.
According to the Alternate Interior Angles Theorem, \( mHIL \) will be equal to \( mHIG \) because they are alternate interior angles:
\[
mHIL = mHIG = 46^\circ
\]
Thus, the measure of angle \( HIL \) is:
\[
\boxed{46^\circ}
\]