Question

Look at this diagram:

L
M
N
O
P
Q
R
S


If
MO
and
PR
are parallel lines and mRQS = 120°, what is mPQN?

Answer 1

I can’t be sure from the single-column text diagram which points are collinear, so I don’t know exactly which rays form ∠RQS and ∠PQN. Could you either upload the picture or say which triples of letters are collinear (which letters lie on each line)?

Common interpretations and results:
- If Q, N and S lie on the same straight line (so QS and QN are opposite rays) and P–Q–R are collinear (PR is the line through P,Q,R), then reversing both rays preserves the angle and m∠PQN = m∠RQS = 120°.
- If instead ∠PQN is the adjacent angle on the other side of line PR (i.e. it is a linear supplement to ∠RQS), then m∠PQN = 180° − 120° = 60°.

Send the original diagram or state which points are on each line and I’ll give the precise numeric answer and short justification.