The question lacks sufficient information in terms of specific angles and side lengths to estimate the measures accurately for the De Young Museum's Entry Court. Typically, the geometric shape would provide clues to determine equivalent angles and sides. More context or a diagram is required for a precise answer.
The question seems to be missing some information, such as the specific angles and side lengths mentioned, and potentially a figure that provides context for the De Young Museum's Entry Court. Typically, to determine reasonable estimates for the measures of each angle and side length, you would require information or a diagram to understand the geometric shape of the Entry Court. If the Entry Court is, for example, rectangular in shape, opposite sides would be equal in length, and all angles would be 90 degrees.
For Part B, equivalent angles and sides would also depend on the specific geometric structure of the Entry Court. If it is rectangular, then m∠B would be equal to m∠D, and AB would be equal to CD, while AE would be equal to DE.
Without the complete details or an accompanying diagram, providing accurate measures is not possible. Generally, proving congruence of angles and sides requires geometrical theorems or axioms, such as side-angle-side or angle-side-angle, among others.
A reasonable estimate for the measure of each angle and side length of the Entry Court in the miniature replica of the De Young Museum can be determined by looking at the given information.
Based on the information in the brochure, the measure of angle A is 45 degrees, angle B is 38 degrees, angle C is 14 degrees, angle D is 316 degrees, and angle E is 14 degrees. Side AB is 38 inches long. Side ED is also 14 inches long. Side lengths for the other sides of the Entry Court are not given.
From the given information, we can conclude that angles B and E are equal, and angles D and C are equal. Angles A and B are not equal. Side ED is equal to side BC. Side AB and side BC are not equal.