Since triangles \(\triangle BCE\) and \(\triangle JKL\) are similar, their corresponding angles are equal.
In triangle \(\triangle BCE\), the angles are given as:
- \(m∠B = 89°\)
- \(m∠C = 13°\)
- \(m∠E = 78°\)
To find \(m∠J\) in triangle \(\triangle JKL\), we can look for the corresponding angle to \(m∠B\).
Since the angles in a triangle must sum up to \(180°\):
\[ m∠B + m∠C + m∠E = 89° + 13° + 78° = 180° \]
From the similarity of the triangles, we conclude:
\[ m∠J = m∠B = 89° \]
Thus,
\[ m∠J = 89° \]
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