Using the Angle-Angle (AA) criterion for similarity, if a triangle is dilated (scaled) by any factor, the angles of the triangle remain the same.
Given that one triangle has angle measures of \(34^\circ\) and \(80^\circ\), to find the third angle, we can use the fact that the sum of the angles in a triangle is \(180^\circ\):
\[ \text{Third angle} = 180^\circ - (34^\circ + 80^\circ) = 180^\circ - 114^\circ = 66^\circ \]
Thus, the angles of the original triangle are \(34^\circ\), \(80^\circ\), and \(66^\circ\).
After dilation, the angles of the new triangle will still be \(34^\circ\), \(80^\circ\), and \(66^\circ\), since dilation does not change the angle measures.
Therefore, the corresponding angles of the dilated triangle are \(34^\circ\) and \(80^\circ\).
So the correct response is:
34 degrees and 80 degrees.
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