Look at this diagram:

Question

L
M
N
O
P
Q
R
S




























If
MO
and
PR
are parallel lines and
m
ONL
= 118°, what is
m
PQS
?

Answer 1

To find \( m \angle PQS \), we can use the information given about the parallel lines \( MO \) and \( PR \).

Since \( MO \) and \( PR \) are parallel, we can apply the concept of alternate interior angles. The angle \( \angle ONL \) (which is given as \( 118^\circ \)) is an interior angle made when a transversal line intersects the two parallel lines.

According to the properties of parallel lines:

• \( \angle ONL \) and \( \angle PQS \) are alternate interior angles.

Thus, because these angles are equal due to the property of alternate interior angles:

\[ m \angle PQS = m \angle ONL = 118^\circ \]

Therefore,

\[ m \angle PQS = 118^\circ \]