Question
If
JL
and
MO
are parallel lines and mLKN = 51°, what is mMNK?
JL
and
MO
are parallel lines and mLKN = 51°, what is mMNK?
Answers
GPT-4o mini
Since JL and MO are parallel lines and LKN is a transversal line, we can apply the properties of parallel lines and transversals.
Given:
- \( m\angle LKN = 51^\circ \)
Because angles on a straight line sum up to 180°, and angles that are on the same side of a transversal between two parallel lines are supplementary, we can find \( m\angle MNK \).
The angle \( MNK \) is alternate interior to angle \( LKN \). Thus, \( m\angle MNK \) is also equal to \( m\angle LKN \).
Therefore,
\[
m\angle MNK = m\angle LKN = 51^\circ.
\]
Thus,
\[
\boxed{51^\circ}.
\]
Given:
- \( m\angle LKN = 51^\circ \)
Because angles on a straight line sum up to 180°, and angles that are on the same side of a transversal between two parallel lines are supplementary, we can find \( m\angle MNK \).
The angle \( MNK \) is alternate interior to angle \( LKN \). Thus, \( m\angle MNK \) is also equal to \( m\angle LKN \).
Therefore,
\[
m\angle MNK = m\angle LKN = 51^\circ.
\]
Thus,
\[
\boxed{51^\circ}.
\]