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°

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet