What is an acute inscribed angle based on a chord equal to the radius of the circle?

We will also draw the points O, the center of the circle, the radii OA and OB.

Since, by condition, the length of the chord AB is equal to the radius of the circle, then AB = OA = OB = R, and therefore the triangle AOB is equilateral.

Then the central angle ARB = 60, and the chord AB contracts the arc, the degree measure of which is 60.

The inscribed angle ACB is equal to half of the degree measure of the arc AB.

Angle ACB = 60/2 = 30.

Answer: The inscribed angle ACB is 30.