Final answer:
The measure of arc BC is 88°.
Step-by-step explanation:
To find the measure of arc BC when given the measure of ∠BAC is 88°, we need to use the properties of circles and the fact that the measure of the angle formed by two chords intersecting inside a circle is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
Since ∠BAC intercepts arcs BC and BAC, and it measures 88°, arc BC and its vertical arc (which is also arc BC due to the symmetry) will sum up to twice the angle's measure.
So, since the measure of angle ZBAC is 88°, we can say that the sum of arcs ZAC and ZBC is 2 × 88° = 176°. Since arcs ZAC and ZBC are opposite each other, they are congruent, meaning they have the same measure.
Therefore, the measure of arc ZBC is 176°/2 = 88°.