Question
If BD and EG are parallel lines and mEFH = 133°, what is mGFC?
Answers
GPT-4o mini
To find the measure of angle \( mGFC \), we can use the properties of parallel lines and transversals.
Since BD and EG are parallel lines, any transversal that crosses them creates corresponding angles that are equal, and alternate interior angles that are also equal.
Assuming that point F is a point where the transversal intersects line BD, and point H is a point where the transversal intersects line EG, \( mEFH \) being \( 133^\circ \) indicates that angle \( EFH \) is an exterior angle to the angle \( GFC \).
Since \( EFH \) and \( GFC \) are on opposite sides of the transversal, they are alternate interior angles. Therefore, they are equal.
Thus,
\[
mGFC = mEFH = 133^\circ.
\]
So, the measure of angle \( GFC \) is \( 133^\circ \).
Since BD and EG are parallel lines, any transversal that crosses them creates corresponding angles that are equal, and alternate interior angles that are also equal.
Assuming that point F is a point where the transversal intersects line BD, and point H is a point where the transversal intersects line EG, \( mEFH \) being \( 133^\circ \) indicates that angle \( EFH \) is an exterior angle to the angle \( GFC \).
Since \( EFH \) and \( GFC \) are on opposite sides of the transversal, they are alternate interior angles. Therefore, they are equal.
Thus,
\[
mGFC = mEFH = 133^\circ.
\]
So, the measure of angle \( GFC \) is \( 133^\circ \).