Look at this diagram:

Question

G
H
I
J
K
L
M
N




























If
HJ
and
KM
are parallel lines and
m
HIL
= 61°, what is
m
MLI
?

Answer 1

To solve for \( m \angle MLI \), we can use the fact that \( HJ \) and \( KM \) are parallel lines and that \( m \angle HIL = 61^\circ \).

Since \( HJ \) and \( KM \) are parallel, the angles formed by a transversal (in this case, line \( IL \)) have special relationships:

1. \( \angle HIL \) and \( \angle MLI \) are alternate interior angles.

By the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the alternate interior angles are equal.

Therefore, we have:

\[ m \angle MLI = m \angle HIL \]

Since \( m \angle HIL = 61^\circ \), it follows that:

\[ m \angle MLI = 61^\circ \]

Thus, the measure of angle \( MLI \) is:

\[ \boxed{61^\circ} \]