Equilateral triangle ABC is inscribed in Circle O. Use the diagram to find the following measures.

m =

a0°

mABC =

a1°

mAOB =

a2°

Since there is no given diagram, I did my own.

So, qualities of an equilateral triangle:

1) all sides have the same measure

2) it is also an equiangular triangle, which means that each interior angles have the same measure. Since the sum of all interior angles are 180°, then each angle is 60°.

When you put an equilateral triangle inside a circle, each of its vertex is "on" the circle. So when you are solving for the measure of the intercepted arc, you simply multiply the measure of the inscribed angle by 2.

Each vertex of the triangle is 60°. Thus, its intercepted arc is 120° ↔ (60° * 2). In the event that the measure of the intercepted arc is given, the inscribed angle is 1/2 of the intercepted arc.

So, when you add up all the intercepted arc of the equilateral triangle it will total 360°, which is the total angle of a circle.