Question

find the measure of ∠b and ∠e in the similar triangles.

Explanation:

Step1: Analyze ∠B

Since \( \angle A \) is a right angle (\( 90^\circ \)) and \( DB \perp AC \), \( \angle B \) is also a right angle. So \( \angle B = 90^\circ \).

Step2: Analyze ∠E

In similar triangles, corresponding angles are equal. Triangle \( EAC \) and triangle \( DBC \) are similar (right triangles with common \( \angle C \)). The sum of angles in a triangle is \( 180^\circ \). In triangle \( DBC \), \( \angle C = 53^\circ \), \( \angle B = 90^\circ \), so \( \angle D = 180^\circ - 90^\circ - 53^\circ = 37^\circ \). Since \( \angle E \) corresponds to \( \angle D \) (or we can calculate in triangle \( EAC \): \( \angle E = 180^\circ - 90^\circ - 53^\circ = 37^\circ \)).

Answer:

\( \angle B = 90^\circ \), \( \angle E = 37^\circ \)