Answer:
(A) [tex]60^{\circ}[/tex]
Step-by-step explanation:
It is given that the arcAC=75° and arcDE=45°, thus using the property that the angle formed by two chords is equal to half of the sum of the intercepted arcs that is:
[tex]{\angle}ABC=\frac{1}{2}(arcAC+arcDE)[/tex]
Substituting the given values, we get
[tex]{\angle}ABC=\frac{1}{2}(75^{\circ}+45^{\circ})[/tex]
[tex]{\angle}ABC=\frac{1}{2}(120^{\circ})[/tex]
[tex]{\angle}ABC=60^{\circ}[/tex]
Hence, the measure of [tex]{\angle}ABC[/tex] is [tex]60^{\circ}[/tex].
Therefore, option A is correct.
