Question

Look at this diagram:


I
J
K
L
M
N
O
P

































If
JL
and
MO
are parallel lines and
m
LKI
= 116°, what is
m
ONP
?

Answer 1

To solve this problem, we need to use the properties of parallel lines and the angles formed by a transversal.

Given that JL and MO are parallel lines and \( mLKI = 116^\circ \), we can observe the configuration of angles formed when a transversal crosses these parallel lines.

Here's how we can deduce \( mONP \):

1. **Identify angles**: Since JL and MO are parallel and assuming that the transversal intersects these lines, then angle LKI (which is inside the transversal lines) will have a corresponding angle formed on the opposite side of the transversal with angle ONP.

2. **Calculate \( mONP \)**: By the properties of corresponding angles, \( mLKI + mONP = 180^\circ \) (since they are supplementary). Therefore, we can write:

\[
mONP = 180^\circ - mLKI
\]

Substituting the value of \( mLKI\):

\[
mONP = 180^\circ - 116^\circ = 64^\circ
\]

Thus, \( mONP = 64^\circ \).