Answer:
m<AEC = 105
Step-by-step explanation:
(just completed the assignment) they are vertical angles, so they have the same measure
The measure of [tex]\angle AEC[/tex] is [tex]105^{o}[/tex].
Vertically opposite angles are the angles formed opposite each other when two lines intersect. Vertically opposite angles are always equal.
According to the given question.
We have a circle with center E and two chords CD and AB.
Also, both the chords intersecting each other and form vertical angles.
Here,
[tex]m\angle DEB = 105^{o}[/tex] (given)
Since, [tex]m\angle DEB[/tex] and [tex]m\angle AEC[/tex] are vertical opposite angles.
Therefore,
[tex]m\angle DEB = m\angle AEC[/tex]
[tex]\implies m\angle AEC = 105^{o}[/tex]
Hence, the measure of [tex]\angle AEC[/tex] is [tex]105^{o}[/tex].
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