Question

figure abcd is the image of figure abcd after a rotation around point e. what is the measure of ∠adc?

Explanation:

Step1: Recall rotation property

Rotation is a rigid transformation, so corresponding angles of the pre - image (ABCD) and image (A'B'C'D') are equal.

Step2: Identify corresponding angle

$\angle A'D'C'$ in the image corresponds to $\angle ADC$ in the pre - image. From the diagram, $\angle ADC = 45^{\circ}$. So, by the property of rotation (corresponding angles are congruent), $\angle A'D'C'=\angle ADC = 45^{\circ}$.

Answer:

$45^{\circ}$