Answer:
∠AEC = 105°
Step-by-step explanation:
If two chords intersect each other in a circle then the vertical angles formed are equal.
In this question two chords AB and CD intersect each other at point E then ∠DEB and ∠AEC are vertical angles which are equal.
Therefore ∠DEB = ∠AEC
Here m∠DEB = 105°
Then m∠AEC = 105° ( by Theorem)
Therefore the correct answer is ∠AEC = 105°
Answer: The measure of angle AEC is 105°.
Step-by-step explanation: Given that in the circle shown in the figure, AB and CD are two chords intersecting at the point E.
And, m∠DEB = 105°.
We are to find the measure of angle AEC.
We can see from the figure that
∠DEB and ∠AEC are vertically opposite angles.
Since the measures of vertically opposite angles are equal, so we must have
[tex]m\angle DEB=m\angle AEC.[/tex]
Since, m∠DEB = 105°, so we get
m∠AEC = 105°.
Thus, the measure of angle AEC is 105°.
