Answer:
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 = [tex]\frac{1}{2}[/tex] m arc BC
∵ m∠BAC = 70°
- Substitute it in the the expression above
∴ 70 = [tex]\frac{1}{2}[/tex] 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 = [tex]\frac{1}{2}[/tex] measure of the circle
- The measure of the circle is 360°
∴ m of arc ACB = [tex]\frac{1}{2}[/tex] (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°
