To determine if the triangles \( \Delta PRQ \) and \( \Delta FGH \) are similar, we can check the angles given.
For \( \Delta PRQ \):
- \( \angle P = 30^\circ \)
- \( \angle R = 127^\circ \)
- To find \( \angle Q \): \[ \angle Q = 180^\circ - \angle P - \angle R = 180^\circ - 30^\circ - 127^\circ = 23^\circ \]
For \( \Delta FGH \):
- \( \angle H = 30^\circ \)
- \( \angle G = 23^\circ \)
- To find \( \angle F \): \[ \angle F = 180^\circ - \angle H - \angle G = 180^\circ - 30^\circ - 23^\circ = 127^\circ \]
Now we have:
- \( \Delta PRQ \): \( \angle P = 30^\circ \), \( \angle R = 127^\circ \), \( \angle Q = 23^\circ \)
- \( \Delta FGH \): \( \angle H = 30^\circ \), \( \angle G = 23^\circ \), \( \angle F = 127^\circ \)
Both triangles have the same set of angles:
- \( \angle P \) corresponds with \( \angle H \)
- \( \angle Q \) corresponds with \( \angle G \)
- \( \angle R \) corresponds with \( \angle F \)
Since both triangles have two pairs of equal angles, we can use the AA (Angle-Angle) criterion for similarity.
Therefore, the correct response is:
AA
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