Find the chord that the 150-degree angle rests on in a circle of radius.

By condition, the inscribed angle ACB resting on the large arc AB is equal to 150, then the degree measure of the larger arc AB is equal to two degree measures of the inscribed angle. Arc AB = 2 * 150 = 300.

The degree measure of the circle is 360, then the arc ACB = 360 – 300 = 60.

Let’s construct the radii ОА and ОВ. ОА = ОВ = 1cm. The central angle AOB rests on the arc ACB, then the angle AOB is equal to the degree measure of the arc ACB. Angle AOB = 60, and then the triangle AOB is equilateral, AB = OA = OB = R = 1 cm.

Answer: The length of the chord AB is 1 cm.