The required measure of XZ (the minor arc) is 116. Option A is correct.
In the figure, a circle gave with 3 arc divisions XY, YZ, and XZ. And angle 58 at point y.
What is a circle?
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by. (x-h)²+(y-k)²=2 where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.
Since by the property of the circle the angle subtended by arc to the vertex corresponding to the center is half the measure of the angle subtended by the arc to the center.
so, let the center of the circle is o.
Now,
measure of XZ = 2 * 58
= 116
Thus, the required measure of XZ (the minor arc) is 116.
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