Answer:
The measure of angle ∠A is 44°
Step-by-step explanation:
Given the measure of angles in the figure
measure of arc DE=124° and arc BC=36°
we have to find the measure of ∠A
By the theorem of intercepted arcs to the angle of two secants which states that
The measure of an angle formed by the two secants from a point outside the circle is half the difference of the intercepted arcs i.e
[tex]m \angle A=\frac{1}{2}(arc DE-arc BC)[/tex]
[tex]\angle A=\frac{1}{2}(\angle DOE-\angle BOC)[/tex]
[tex]\angle A=\frac{1}{2}(124^{\circ}-36^{\circ})=\frac{1}{2}\times 88=44^{\circ}[/tex]
The measure of angle ∠A is 44°
Option A is correct.
