D.4 Transversals of parallel lines: find angle measures

Question

WB9

Look at this diagram:

L
M
N
O
P
Q
R
S

If
MO
and
PR
are parallel lines and mONQ= 127°, what is mPQN?

Answer 1

To find \( mPQN \) given that \( MO \) and \( PR \) are parallel lines and \( mONQ = 127° \), we can use the properties of angles formed by transversals.

Since \( MO \) and \( PR \) are parallel lines, the angle \( ONQ \) (which is 127°) and the angle \( PQN \) are corresponding angles. Corresponding angles are equal when a transversal crosses parallel lines.

Thus, we can conclude that:

\[ mPQN = mONQ = 127° \]

Therefore, \( mPQN \) is \( 127° \).