Option D:
Measure of arc BEC = 228°
Solution:
Given angle A = 114° and vertical angle of A = 0.
If two chords intersect inside the circle, then the measure of each angle is one half of the sum of the measures of the arcs intercepted by the angle and its vertical angle.
[tex]$\Rightarrow \angle A = \frac{1}{2} (ar \ BEC + vertical \ ar A)[/tex]
[tex]$\Rightarrow 114^\circ = \frac{1}{2} (ar \ BEC + 0)[/tex]
[tex]$\Rightarrow 114^\circ = \frac{1}{2} (ar \ BEC)[/tex]
Multiply by 2 on both sides, we get
[tex]$\Rightarrow 2\times 114^\circ = 2\times \frac{1}{2} (ar \ BEC)[/tex]
[tex]$\Rightarrow 228^\circ = (ar \ BEC)[/tex]
Measure of arc BEC = 228°
Option D is the correct answer.
