To find the pairs of congruent corresponding angles in triangles \( \triangle MNO \) and \( \triangle RTS \), we will compare the measures of the angles in both triangles.
Given:
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In \( \triangle MNO \):
- \( m\angle M = 78^\circ \)
- \( m\angle N = 34^\circ \)
- \( m\angle O = 68^\circ \)
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In \( \triangle RTS \):
- \( m\angle S = 68^\circ \)
- \( m\angle R = 78^\circ \)
- \( m\angle T = 34^\circ \)
Now, let's match corresponding angles between the two triangles:
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\( m\angle M \) and \( m\angle R \):
- \( m\angle M = 78^\circ \) and \( m\angle R = 78^\circ \)
- These two angles are congruent: \( \angle M \cong \angle R \).
-
\( m\angle N \) and \( m\angle T \):
- \( m\angle N = 34^\circ \) and \( m\angle T = 34^\circ \)
- These two angles are congruent: \( \angle N \cong \angle T \).
-
\( m\angle O \) and \( m\angle S \):
- \( m\angle O = 68^\circ \) and \( m\angle S = 68^\circ \)
- These two angles are congruent: \( \angle O \cong \angle S \).
Conclusion: The pairs of congruent corresponding angles are:
- \( \angle M \cong \angle R \)
- \( \angle N \cong \angle T \)
- \( \angle O \cong \angle S \)
This shows that the triangles are similar by the Angle-Angle (AA) similarity postulate, as they have pairs of congruent angles.