To solve the problem, we need to understand the relationships between the angles formed by the parallel lines and the transversal lines that intersect them.
Given that \( JL \) and \( MO \) are parallel lines and \( m\angle MNK = 63^\circ \), we can infer the following relationships:
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Corresponding Angles: When a transversal intersects two parallel lines, the corresponding angles formed on the same side of the transversal are equal.
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Alternate Interior Angles: When a transversal crosses two parallel lines, the alternate interior angles are equal.
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Consecutive Interior Angles: Together, these angles add up to \( 180^\circ \).
Since we need to find \( m\angle ONP \) and given that angle \( MNK \) is formed by line \( JK \) which intersects the parallel lines \( JL \) and \( MO \), we identify that angle \( ONP \) corresponds to angle \( MNK \).
Since \( m\angle MNK = 63^\circ \), angle \( ONP \) will also equal \( 63^\circ\) because they are corresponding angles:
\[ m\angle ONP = m\angle MNK = 63^\circ \]
Thus, the answer is:
\[ \boxed{63^\circ} \]