When a triangle is dilated, the angles of the triangle do not change. The AA (Angle-Angle) criterion states that if two triangles have two angles that are congruent, then the triangles are similar.
Since the triangle with angle measures of 34 degrees and 80 degrees has a third angle that can be calculated as follows:
\[ \text{Third angle} = 180^\circ - (34^\circ + 80^\circ) = 180^\circ - 114^\circ = 66^\circ \]
The angles of the original triangle are 34 degrees, 80 degrees, and 66 degrees. After applying a dilation of 2 centered at the origin, the dilated triangle will have the same angle measures.
Thus, the two corresponding angles of the dilated triangle will also be:
- 34 degrees
- 80 degrees
And the third angle will remain as 66 degrees. So, the corresponding angles of the dilated triangle are 34 degrees, 80 degrees, and 66 degrees.