Given that the triangles \( \triangle GHI \) and \( \triangle LKI \) are similar (denoted as \( \triangle GHI \sim \triangle LKI \)), the corresponding angles of similar triangles are equal.
From the problem, we know the following measures for triangle \( GHI \):
- \( m\angle G = 30^\circ \)
- \( m\angle H = 80^\circ \)
- \( m\angle I = 70^\circ \)
Since the angles of triangle \( LKI \) correspond to the angles of triangle \( GHI \) due to their similarity, we can determine the measures of angles \( L \), \( K \), and \( J \) as follows:
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Corresponding to \( m\angle G = 30^\circ \), we have: \[ m\angle L = m\angle G = 30^\circ \]
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Corresponding to \( m\angle H = 80^\circ \), we have: \[ m\angle K = m\angle H = 80^\circ \]
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Corresponding to \( m\angle I = 70^\circ \), we have: \[ m\angle J = m\angle I = 70^\circ \]
Thus, the measures of angles \( J \), \( K \), and \( L \) are:
- \( m\angle J = 70^\circ \)
- \( m\angle K = 80^\circ \)
- \( m\angle L = 30^\circ \)
To summarize:
- \( m\angle J = 70^\circ \)
- \( m\angle K = 80^\circ \)
- \( m\angle L = 30^\circ \)
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