Relate central angles, inscribed angles, and their intercepted arcs.
A central angle has its vertex at the center of the circle and equals the measure of its intercepted arc. An inscribed angle has its vertex on the circle and equals half the measure of its intercepted arc.
All inscribed angles that intercept the same arc are equal. An inscribed angle in a semicircle is always 90°.
A circle has radius 6 cm and a central angle of 120°. Convert to radians: 120° · π/180 = 2π/3. Arc length = 6 · (2π/3) = 4π ≈ 12.57 cm.
Remember This!
Always convert degrees to radians when using the arc length and sector area formulas with radians: multiply by π/180. Or use the degree formula directly.
A central angle intercepts an arc of 140°. What is the measure of an inscribed angle intercepting the same arc?