Question

“Triangle ABC is equilateral. What is the measure of arc AB?” This question doesn’t have any angles or anything, how do I solve this?

Answer 1

It can be solved with the help of the attached figure
As shown in the figure Triangle ABC is equilateral

So, the measure of each angle of the triangle = 60°
By drawing a circle of center M so that the vertices of the triangle lie on the circle ∴ M will be the center of the triangle

The measure of arc AB = the measure of angle ∠ AMB = 2 *∠ ACB
= 2 * 60 = 120°
convert to radian = 120 * π /180 = (2/3) π

If we want to measure the length of the arc AB = [(2/3)π] * radius
Radius = (1/3) height of triangle = (1/3) * (√3/2) x
Where x is the length of the side of the triangle.