The measure of ∠ABC is 88.
From the diagram, it exists clearly visible that the angle ∠ABC exists created by intersections of two chords AE and CD of the circle.
We know the following formula for angles created in circles:-
The angle created by two intersecting chords of a circle = Half the sum of intersecting arcs.
∠ABD = 0.5( arc AD + arc EC)
∠ABD = 0.5(131 + 53)
∠ABD = 0.5 × 184
∠ABD = 92°
∠ABD and ∠ABC form a straight angle, thus
92 + ∠ABC = 180 ( subtract 92 from both sides )
∠ABC = 88°
Therefore, the correct answer is option (c), 88.
To learn more about the chords of a circle
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