Let's consider the geometrical properties of a parallelogram and the effect of translations on these properties.
Firstly, it's important to understand that in a parallelogram, opposite angles are equal. This gives us:
- Angle \( A = 110^\circ \)
- Angle \( C = 110^\circ \) (since \( C \) is opposite to \( A \))
Secondly, consecutive angles in a parallelogram are supplementary, meaning they add up to \( 180^\circ \):
- Angle \( A + \) Angle \( B = 180^\circ \)
- Given Angle \( A = 110^\circ \), so Angle \( B = 180^\circ - 110^\circ = 70^\circ \)
Now, John translates the parallelogram ABCD using the rule \((x, y) \rightarrow (x+3, y-2)\).
A translation of a shape in the coordinate plane means moving every point of the shape the same distance in the same direction. Importantly, a translation does not change the shape's size, angles, or side lengths. It simply shifts the entire figure to a new location.
Therefore, all angles in the parallelogram remain the same after translation. So, the angle \( A^\prime \) (which is the image of angle \( A \) after translation) will have the same measure as the original angle \( A \).
Thus, the degree measurement of angle \( A^\prime \) is \( 110^\circ \).
Therefore, the answer is:
[tex]\[ 110^\circ \][/tex]
