Question

Look at this diagram:

K
L
M
N
O
P
Q
R


If
LN
and
OQ
are parallel lines and mOPM= 121°, what is mQPM?

Answer 1

To find \( mQPM \), we can utilize the property of parallel lines and a transversal.

Since \( LN \) and \( OQ \) are parallel lines, and \( OP \) acts as a transversal that intersects both lines, we have two angles formed at points \( P \) on each line.

The angle \( mOPM \) is given as \( 121^\circ \). The angle \( mQPM \) is the angle on the opposite side of the transversal at the same point \( P \). According to the property of alternate interior angles (since \( LN \) and \( OQ \) are parallel), \( mQPM \) and \( mOPM \) are supplementary angles.

This means:

\[
mQPM + mOPM = 180^\circ
\]

Substituting the value of \( mOPM \):

\[
mQPM + 121^\circ = 180^\circ
\]

To find \( mQPM \):

\[
mQPM = 180^\circ - 121^\circ = 59^\circ
\]

Thus, \( mQPM = 59^\circ \).