The measure of arc AC is 40° Step-by-step explanation: In any circle the measure of an inscribed angle is one-half the measure of its subtended arc In circle O ∵ ∠BAC is an inscribed angle subtended by arc BC ∴ m∠BAC = m arc BC ∵ m∠BAC = 70° - Substitute it in the the expression above ∴ 70 = m arc BC - Multiply both sides by 2 ∴ 140 = m arc BC ∴ The measure of arc BC is 140° ∵ AB is a diameter - The diameter divides the circle into two equal arcs ∴ m of arc ACB = measure of the circle - The measure of the circle is 360° ∴ m of arc ACB = (360°) ∴ m of arc ACB = 180° ∵ m arc BC + m arc AC = m arc ACB ∴ 140° + m arc AC = 180° - Subtract 140 from both sides ∴ m arc AC = 40° The measure of arc AC is 40°