Since the triangles \( \triangle GHI \) and \( \triangle LJK \) are similar (indicated by \( \triangle GHI \sim \triangle LJK \)), the corresponding angles of the two triangles are equal.
Given:
- \( m\angle G = 30^\circ \)
- \( m\angle H = 80^\circ \)
- \( m\angle I = 70^\circ \)
First, let's verify that the angles in \( \triangle GHI \) sum to \( 180^\circ \):
\[ m\angle G + m\angle H + m\angle I = 30^\circ + 80^\circ + 70^\circ = 180^\circ \]
Now, since the triangles are similar, we can determine the angles in \( \triangle LJK \):
- \( m\angle L = m\angle G = 30^\circ \)
- \( m\angle J = m\angle H = 80^\circ \)
- \( m\angle K = m\angle I = 70^\circ \)
Thus, the measures of angles \( J \), \( K \), and \( L \) are as follows:
- \( m\angle L = 30^\circ \)
- \( m\angle J = 80^\circ \)
- \( m\angle K = 70^\circ \)
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