circles: central angles & arc measure tutorial 8b
TRANSCRIPT
Circles: Central Angles & Arc Measure
Tutorial 8bTutorial 8b
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.
P
Circle PCircle P
C
A
BCentral Angle = APBAPB
D Semicircle = CDBCDB “ ” is a symbol for arc.
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.
Minor arcs below are: AB or ACAB or AC
P
Circle PCircle P
C
A
B
D
The measure of arc AB is equal to the measure of APB. This can be written using the following symbols:
mmAB = 135AB = 135ºº
135135ºº
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.
Major arc = ACB or BDAACB or BDA
P
Circle PCircle P
C
A
B
D
Central Angles and Arcs
Adjacent arcs are two arcs in the same circle that have exactly one point in common.
Adjacent arcs: AC & AB orAC & AB or
AB & BDAB & BDP
Circle PCircle P
C
A
B
D
Central Angles and Arcs
Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the two arcs.
P
Circle PCircle P
C
A
B
D
mAB + mBD = mAD mAB + mBD = mAD Example:
mAB + mBD = mAD mAB + mBD = mAD
85º
45º
85º + 45º = 130º
mAD = 130 º
70 20
160 360 - 90 = 270
180 - 36 = 144 36
36180
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Click toCheck answers
Click toCheck answers
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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 tocheck your answers
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1. Potatoes: 8.8% of 360º = 31.68º2. Green beans: 11.9% of 360º = 42.84º3. Corn: 15.1% of 360º = 54.36º4. Carrots: 10.8% of 360º = 38.88º5. Broccoli: 19.7% of 360º = 70.92º
