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

From the center of the circle O draw the radii of the circle OA and OB.
The AOB triangle is equilateral, since the chord AB is equal in length to the radius of the circle.
In an isosceles triangle, all interior angles are 60, then the central angle AOB = 60, and therefore the degree measure of the smaller arc AB is 60.
The value of the inscribed angle CAB is equal to half of the degree measure of the arc on which this angle rests.
Angle ACB = AB / 2 = 60/2 = 30.
Answer: The inscribed angle is 30.