Circles: Central Angles & Arc Measure

Circles: Central Angles & Arc Measure Tutorial 8b

Central Angle =  APB Semicircle = CDB “ ” is a symbol for arc. Central Angles and Arcs • A central angle is an angle whose vertex is at the center of the circle. • A semicircle is a half circle. The measure of a semicircle is 180. A Circle P C B P D

Central Angles and Arcs • A minor arc is shorter than a semicircle. The measure of a minor arc is the measure of its corresponding central angle. Circle P Minor arcs below are: AB or AC A The measure of arc AB is equal to the measure of APB.This can be written using the following symbols: 135º C B P D mAB = 135º

Central Angles and Arcs • A major arc is longer than a semicircle. The measure of a major arc is the 360 minus the measure of its related minor arc. A Circle P Major arc = ACB or BDA C B P D

Central Angles and Arcs • Adjacent arcs are two arcs in the same circle that have exactly one point in common. A Circle P Adjacent arcs: AC & AB or AB & BD C B P D

mAB + mBD = mAD mAB + mBD = mAD mAD = 130 º Central Angles and Arcs • Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the two arcs. A Circle P 85º C B Example: P 45º D 85º + 45º = 130º

1. 70 20 2. 3. 160 4. 360 - 90 = 270 5. 180 - 36 = 144 6. 36 7. 180 8. 36 Click to Check answers

1. 2. 3. 4. 5. Since there are 360º in a circle, simply multiply each percent by 360 to find the measure of each central angle in the graph. Click here to check your answers

1. 2. 3. 4. 5. • Potatoes: 8.8% of 360º = 31.68º • Green beans: 11.9% of 360º = 42.84º • Corn: 15.1% of 360º = 54.36º • Carrots: 10.8% of 360º = 38.88º • Broccoli: 19.7% of 360º = 70.92º

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Circles: Central Angles & Arc Measure