Question

1. in the figure below, \\( \angle aed \\) is a right angle. what is the measure of \\( \angle aeb? \\) a) \\( 45 ^ { \circ } \\) b) \\( 50 ^ { \circ } \\) c) \\( 55 ^ { \circ } \\) d) \\( 60 ^ { \circ } \\) e) \\( 65 ^ { \circ } \\)

Explanation:

Step1: Determine the sum of angles

Since \(\angle AED = 90^{\circ}\) (right - angle), and \(\angle AEB+\angle BEC+\angle CED=\angle AED\).

Step2: Substitute the known angles

We know \(\angle BEC = 25^{\circ}\) and \(\angle CED=15^{\circ}\). Let \(\angle AEB=x\). Then \(x + 25^{\circ}+15^{\circ}=90^{\circ}\).

Step3: Solve for \(x\)

\(x=90^{\circ}-(25^{\circ} + 15^{\circ})\).
\(x=90^{\circ}-40^{\circ}\).
\(x = 50^{\circ}\).

Answer:

B. \(50^{\circ}\)