Let's assume x is the arc measure of arc AC we're after.
Since CD is a diameter, it divides the circle in two, so the upper half arc is 180°.
Since we're parallel, arc AC is congruent to BD, so both measure x.
So for our semicircular arc we have
x + x + 80° = 180°
2x = 100°
x = 50°
Answer: 50°
