Answer:
![m\angle BED = 34^\circ](https://img.qammunity.org/2021/formulas/mathematics/high-school/2pfc4ba09r7iuq6sbpoy676yavisnyxzdy.png)
Explanation:
Angles in a Circle
We need to recall some basic concepts.
An inscribed angle is the angle formed in the interior of a circle when two secant lines intersect.
An arc of a circle is a portion of the circumference of the circle.
Theorem: Inscribed angles subtended by the same arc are equal.
In the figure provided, the points BD form an angle of 34° and the arc BD.
Similarily, arc BD also has two secants BE and DE that form the angle BED.
Thus, applying the above theorem, angle BED and 34° are subtended by the same arc, and the measure of BED is also 34°
![\mathbf{m\angle BED = 34^\circ}](https://img.qammunity.org/2021/formulas/mathematics/high-school/sc3dhurnnm54u1k59iss3nldgqbvu1f4yv.png)