Arc measure and arc length

Learning Objectives Distinguish between arc measure (in degrees) and arc length (in linear units). Calculate the measure of minor arcs, major arcs, and semicircles. Apply the Arc Addition Postulate to find the measure of an arc formed by two adjacent arcs. Derive and apply the formula for arc length. Solve for the radius or central angle of a circle given an arc length. Apply arc measure and arc length concepts to solve multi-step problems. Have you ever wondered if the crust on a large slice of pizza is longer than the crust on a small slice, even if they're cut at the same angle? 🍕 Let's find out! This tutorial explores two fundamental ways to describe a piece of a circle: its measure in degrees and its actual length. Understanding the difference is crucial for...

TermDefinitionExample Central AngleAn angle whose vertex is the center of a circle and whose sides are two radii of the circle.In a circle with center P, if A and B are points on the circle, then ∠APB is a central angle. ArcAn unbroken part of the circumference of a circle.A piece of the crust on a circular pizza is an arc. Arc MeasureThe measure of an arc in degrees, which is equal to the measure of its corresponding central angle. It describes the 'amount of turn' of the arc.If central angle ∠APB measures 60°, then the measure of arc AB is 60°. Arc LengthThe distance along the curved line of the arc. It is a fraction of the circle's total circumference, measured in linear units like cm, inches, or meters.On a circle with a circumference of 30 cm, a 60° arc would have an a...

Arc Measure Rule The measure of a minor arc is equal to the measure of its central angle. The measure of a major arc is 360° minus the measure of its related minor arc. Use this to find the degree measure of any arc when you know the central angle. Remember that a full circle is 360°. Arc Addition Postulate m(arc ABC) = m(arc AB) + m(arc BC) The measure of an arc formed by two adjacent arcs (arcs that share an endpoint) is the sum of the measures of the two individual arcs. This is similar to the Segment Addition and Angle Addition Postulates. Arc Length Formula L = (\frac{\theta}{360}) \cdot 2\pi r Use this formula to calculate the physical length of an arc. 'L' is the arc length, 'θ' (theta) is the measure of the central angle in degrees, and &#...