What is the Relationship Between Arcs and Central Angles?

A central angle has its vertex at the center of a circle, and it equals the measure of the arc it intercepts exactly. That one-to-one relationship is the foundation for every other arc and angle rule.

• Arc: An arc is a segment or a portion of the circumference of a circle.
• Central Angle: It is an angle whose vertex is at the center of the circle and whose sides intercept an arc on the circle.

Worked examples: arcs and central angles

Practice questions on arcs and central angles

1. In a circle with a radius of (5 text{ cm}), what is the length of the arc intercepted by a central angle of (45^circ)?
2. A circle has a central angle that intercepts an arc of (20 text{ cm}) in length. If the circle’s radius is (8 text{ cm}), what is the measure of the central angle?

1. ( frac{45}{360} times (2pi times 5) approx 3.93 text{ cm})
2. ( left( frac{20}{16pi} right) times 360 approx 143.31^circ )

The Ultimate Algebra Bundle 2026 From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

The Ultimate Elementary School Math Bundle Grade 3-5

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.