The chord divides the circle into arcs, the measures of which are 5: 7.

The chord divides the circle into arcs, the measures of which are 5: 7. Determine the degree measures of the inscribed angles based on this chord.

Let the degree measure of one arc formed by the chord AB be equal to 5 * X0, then the degree measure of the other arc will be 7 * X0.

Since the degree measure of the circle is 360, then 5 * X + 7 * X = 360.

12 * X = 360.

X = 360/12 = 30.

Then the smaller arc is 5 * 30 = 150, the larger arc is 7 * 30 = 210.

The inscribed angle is equal to half of the degree measure of the arc on which it rests, then the angle ACB = 210/2 = 105, the angle ADB = 150/2 = 75.

Answer: The inscribed angles are 75 and 105.