D.4 Transversals of parallel lines: find angle measures

Question

WB9 on IXL

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 solve for the measure of angle \( mPQN \), we can use the property of alternate interior angles.

Given that lines \( MO \) and \( PR \) are parallel, angle \( mONQ \) and angle \( mPQN \) are alternate interior angles.

Since \( mONQ = 127° \), the measure of the angle \( mPQN \) will be equal to \( mONQ \) because alternate interior angles are congruent when two parallel lines are cut by a transversal.

Thus, we have: \[ mPQN = mONQ = 127° \]

Therefore, the measure of angle \( mPQN \) is \( 127° \).