Arcs and Central Angles

An arc is a portion of the circumference of a circle, defined by two endpoints on the circle.

A central angle is an angle whose vertex is at the center of the circle and whose sides intersect the circle.

The measure of an arc is equal to the measure of the central angle that subtends it.

A minor arc is an arc that measures less than 180 degrees.

A major arc is an arc that measures more than 180 degrees.

The measure of the central angle ∠AOB is also 142°.

The measure of an arc is equal to the measure of its corresponding central angle.

The measure of arc AOC is 150° (360° - 210°).

Length of arc = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

A semicircle is an arc that measures exactly 180°, while a minor arc measures less than 180°.