Key Concepts: Measuring Angles and Arcs

Central Angle

A central angle has its vertex at the center of the circle. Its measure equals the measure of its intercepted arc.

Types of Arcs

• Minor arc: less than 180° (named by two letters, e.g., AB).
• Major arc: greater than 180° (named by three letters, e.g., ADB).
• Semicircle: exactly 180° (the endpoints are the endpoints of a diameter).

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Arc Length

Arc length = (θ/360°) × 2πr