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Measuring Arcs and Central Angles

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Measuring Arcs Arcs can be measured in two ways, by their length, or by degree For now, we will be measuring arcs only by degree.

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Consider a whole circle In a whole circle, there are 360 degrees. A half circle, the arc between the end points of the diameter, measures 180 ̊.

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Now, think about this…. If I cut the circle in half again, the new arc is 90 ̊. And the angle formed by the perpendicular diameters is a right angle … 90 ̊

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Which Brings Us To……… THE CENTRAL ANGLE THEOREM! Remember: a CENTRAL ANGLE is an angle whose vertex is the center of the circle.

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Central Angle Theorem The arc captured by the rays of a central angle has the same degree as that angle. 90 ̊

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Central Angle Theorem The arc captured by the rays of a central angle has the same degree as that angle. 62 ̊ 120 ̊ 175 ̊

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Assignment Pages 607-608 #20-38 skip #35

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6.3 – 6.4 Properties of Chords and Inscribed Angles.

6.3 – 6.4 Properties of Chords and Inscribed Angles.

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