Question

in the diagram below, line \\( \overleftrightarrow{ae} \\) and \\( \overleftrightarrow{bc} \\) are perpendicular.

diagram showing lines ae (horizontal), bc (vertical), and bd making a 19° angle with bc, with a right angle at b between ae and bc

what is the measure of \\( \angle dbe \\)?

Explanation:

Step1: Identify right angle

Since \( AE \perp BC \), \( \angle CBE = 90^\circ \).

Step2: Calculate \( \angle DBE \)

\( \angle CBE = \angle CBD + \angle DBE \), so \( \angle DBE = \angle CBE - \angle CBD \).
Given \( \angle CBD = 19^\circ \), \( \angle DBE = 90^\circ - 19^\circ = 71^\circ \).

Answer:

\( 71^\circ \)