Question

Look at this diagram:

K
L
M
N
O
P
Q
R


If
LN
and
OQ
are parallel lines and mLMK= 130°, what is mNMP?

Answer 1

Since \( LN \) and \( OQ \) are parallel lines, we can use the properties of angles formed when a transversal crosses parallel lines.

In this case, angle \( LMK \) and angle \( NMP \) are alternate interior angles because:

- \( LN \) (line containing points L and N) is one of the parallel lines.
- \( OQ \) (line containing points O and Q) is the other parallel line.
- Line \( MK \) serves as a transversal.

Given that \( mLMK = 130^\circ \), we can find \( mNMP \):

\[
mNMP = mLMK
\]
Since \( mLMK \) is given as \( 130^\circ \):

\[
mNMP = 130^\circ
\]

Thus, the measure of angle \( NMP \) is \( 130^\circ \).