Question
If HJ and KM are parallel lines and mJIL = 56°, what is mHIL?
Answers
GPT-4o mini
If lines HJ and KM are parallel, then the angles formed when a transversal intersects these lines maintain certain relationships.
Given that \( m\angle JIL = 56^\circ \), and knowing that \( HJ \) and \( KM \) are parallel, we can conclude that \( \angle HIL \) is equal to \( \angle JIL \) due to the Alternate Interior Angles Theorem.
Thus,
\[
m\angle HIL = m\angle JIL = 56^\circ.
\]
So, the measure of angle \( HIL \) is \( 56^\circ \).
Given that \( m\angle JIL = 56^\circ \), and knowing that \( HJ \) and \( KM \) are parallel, we can conclude that \( \angle HIL \) is equal to \( \angle JIL \) due to the Alternate Interior Angles Theorem.
Thus,
\[
m\angle HIL = m\angle JIL = 56^\circ.
\]
So, the measure of angle \( HIL \) is \( 56^\circ \).