Question

if segment \\( \overline { a c } \\) is a diameter, what is the measure of \\( \angle a e d \\)?
\\( \bigcirc \\) a \\( 45 ^ { \circ } \\)
\\( \bigcirc \\) b \\( 67 ^ { \circ } \\)
\\( \bigcirc \\) c \\( 180 ^ { \circ } \\)
\\( \bigcirc \\) d \\( 90 ^ { \circ } \\)

Explanation:

Step1: Recall the property of a diameter and a chord

If a diameter is perpendicular to a chord, then it bisects the chord. In the given circle, since \(AC\) is a diameter and \(DE = EB\) (the marks on the chord \(DB\) indicate they are equal), then \(AC\perp DB\) at point \(E\).

Step2: Determine the measure of \(\angle AED\)

When two lines are perpendicular, the angle between them is \(90^{\circ}\). So, \(\angle AED = 90^{\circ}\)

Answer:

d. \(90^{\circ}\)