Question
Look at this diagram:
L
M
N
O
P
Q
R
S
If
MO
and
PR
are parallel lines and mONQ= 66°, what is mMNQ?
L
M
N
O
P
Q
R
S
If
MO
and
PR
are parallel lines and mONQ= 66°, what is mMNQ?
Answers
GPT-4o mini
In the given scenario, we have two parallel lines, \( MO \) and \( PR \), and we know that \( m \angle ONQ = 66^\circ \).
By the properties of parallel lines and the angles formed by a transversal (in this case, line \( NQ \)), the angles formed are related as follows: the alternate interior angles are equal, and the corresponding angles are also equal.
In this diagram:
- Since \( MO \) and \( PR \) are parallel, and \( NQ \) intersects them, \( m \angle MNQ \) will be equal to \( m \angle ONQ \).
Thus, we have:
\[
m MNQ = m ONQ = 66^\circ.
\]
Therefore, \( m MNQ = 66^\circ \).
By the properties of parallel lines and the angles formed by a transversal (in this case, line \( NQ \)), the angles formed are related as follows: the alternate interior angles are equal, and the corresponding angles are also equal.
In this diagram:
- Since \( MO \) and \( PR \) are parallel, and \( NQ \) intersects them, \( m \angle MNQ \) will be equal to \( m \angle ONQ \).
Thus, we have:
\[
m MNQ = m ONQ = 66^\circ.
\]
Therefore, \( m MNQ = 66^\circ \).