As shown in the diagram below, AB is a diameter
of circle O, and chord AC is drawn.
If m∠BAC = 70, then mAC is

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°

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step-by-step explanation: