169_186_CC_A_RSPC1_C12_662330.indd



10-2 Study Guide and InterventionMeasuring Angles and Arcs3943350127635Angles and Arcs A central angle is an angle whose vertex is at the center of a circle and whose sides are radii. A central angle separates a circle into two arcs, a major arc and a minor arc.Here are some properties of central angles and arcs.? The sum of the measures of the central angles of a circle with no interior points in common is 360.? The measure of a minor arc is less than 180 and equal to the measure of its central angle.? The measure of a major arc is 360 minus the measure of the minor arc.? The measure of a semicircle is 180.? Two minor arcs are congruent if and only if their corresponding central angles are congruent.? The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. (Arc Addition Postulate)GF is a minor arc.CHG is a major arc.∠GEF is a central angle.m∠HEC + m∠CEF + m∠FEG + m∠GEH = 360mCF = m∠CEFmCGF = 360 – mCFCF ? FG if and only if ∠CEF ? ∠FEG.mCF + mFG = mCG401955034925Example: AC is a diameter of ?R. Find mAB and mACB.∠ARB is a central angle and m∠ARB = 42, so mAB = 42.Thus mACB = 360 – 42 or 318.ExercisesFind the value of x.276225-19052495550-19051.2.4410075187960BD and AC are diameters of ?O. Identify each arc as a major arc, minor arc, or semicircle of the circle. Then find its measure.3. mBA 4. mBC5. mCD 6. mACB7. mBCD 8. mAD10-2 Study Guide and Intervention (continued)Measuring Angles and Arcs5478556148702Arc Length An arc is part of a circle and its length is a part of the circumference of the circle.The length of arc ? can be found using the following equation:? = x360 ? 2πrExample: Find the length of AB. Round to the nearest hundredth.5513705102465The length of arc AB, can be found using the following equation: AB = x360 · 2πrAB = x360 · 2πr Arc Length EquationAB = 135360 · 2π(8) SubstitutionAB ≈ 18.85 in. Use a calculator.ExercisesUse ?O to find the length of each arc. Round to the nearest hundredth.54933851314451. DE if the radius is 2 meters2. DEA if the diameter is 7 inches3. BC if BE = 24 feet4. CBA if DO = 3 millimetersUse ?P to find the length of each arc. Round to the nearest hundredth.54768751606555. RT, if MT = 7 yards6. MR, if PR = 13 feet7. MST, if MP = 2 inches8. MRS, if PS = 10 centimeters ................
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