Question
Look at this diagram:
L
M
N
O
P
Q
R
S
If
MO
and
PR
are parallel lines and mMNQ= 119°, what is mPQS?
L
M
N
O
P
Q
R
S
If
MO
and
PR
are parallel lines and mMNQ= 119°, what is mPQS?
Answers
GPT-4o mini
Given that \( MO \) and \( PR \) are parallel lines and \( m\angle MNQ = 119^\circ \), we need to find \( m\angle PQS \).
Since \( MO \) and \( PR \) are parallel lines and \( MN \) is a transversal, we can apply the concept of alternate interior angles. The angle \( \angle MNQ \) corresponds to \( \angle PQS \) due to the properties of angles formed by a transversal cutting through two parallel lines.
Thus, the measure of \( \angle PQS \) is:
\[
m\angle PQS = m\angle MNQ = 119^\circ
\]
Therefore, \( m\angle PQS = 119^\circ \).
Since \( MO \) and \( PR \) are parallel lines and \( MN \) is a transversal, we can apply the concept of alternate interior angles. The angle \( \angle MNQ \) corresponds to \( \angle PQS \) due to the properties of angles formed by a transversal cutting through two parallel lines.
Thus, the measure of \( \angle PQS \) is:
\[
m\angle PQS = m\angle MNQ = 119^\circ
\]
Therefore, \( m\angle PQS = 119^\circ \).