Question

Equilateral triangle ABC is inscribed in circle X. What is the measure of arc CB?

Answer 1

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.

Answer 2

Answer: 120 degrees

===========================================================

Step-by-step explanation:

An equilateral triangle has three sides of the same length, which in turn means that the curved arc pieces AB, BC and AC are the same length (but longer than each side of the triangle).

Furthermore, it leads to the fact that we split a 360 degree circle into three equal portions of 360/3 = 120 degrees each.

Imagine we drew in the line segments AX, BX, and CX. This splits the circle into 3 equal pie slices. Central angle BXC is 120 degrees because of the earlier calculation done before.