Final answer:
In an equilateral triangle inscribed in a circle, each interior angle of the triangle is 60 degrees, dividing the circle into three equal arcs. Therefore, the measure of arc CB is one third of 360 degrees, which is 120 degrees.
Step-by-step explanation:
To determine the measure of arc CB in an equilateral triangle ABC inscribed in a circle, we must recall a few properties of a circle and an equilateral triangle:
- An equilateral triangle has all three interior angles equal, each being 60 degrees.
- The vertices of the triangle are points on the circle, and the sides subtend the arcs of the circle.
- Since the triangle is equilateral, the arcs opposite to each side would also be equal.
Considering these properties, since the sum of the arcs is the full circle which is 360 degrees, each arc is one third of the full circle because the triangle divides the circle into three equal arcs.
Therefore, the measure of arc CB is:
360 degrees / 3 = 120 degrees
The measure of arc CB in an equilateral triangle inscribed in circle X is 120 degrees.