Look at this diagram:

Question

I
J
K
L
M
N
O
P




























If
JL
and
MO
are parallel lines and
m
JKI
= 66°, what is
m
JKN
?

Answer 1

To find the measure of angle \( m\angle JKN \), let's use the information given in the problem.

We know that lines \( JL \) and \( MO \) are parallel, and angle \( JKI \) measures \( 66^\circ \). Because \( JL \) and \( MO \) are parallel lines, we can use the properties of parallel lines and the corresponding angles.

Since \( JK \) is a transversal that intersects the parallel lines \( JL \) and \( MO \), then by the property of corresponding angles, we can deduce the following:

• \( m\angle JKI \) (which is given as \( 66^\circ \)) and \( m\angle JKN \) are corresponding angles when line \( JK \) crosses lines \( JL \) and \( MO \).

Thus, \( m\angle JKN \) also measures \( 66^\circ \).

In conclusion: \[ m\angle JKN = 66^\circ \]