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10.2 Measuring Angles and Arcs

10.2 Measuring Angles and Arcs. Sum of central angles = 360 Minor Arc < 180 Major Arc > 180 Semicircle = 180 Minor Arcs named with the endpoints Major Arcs and semicircles names with the endpoints and one point in-between. A Central Angle. A. D. C. B. E.

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10.2 Measuring Angles and Arcs

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  1. 10.2 Measuring Angles and Arcs • Sum of central angles = 360 • Minor Arc < 180 • Major Arc > 180 • Semicircle = 180 • Minor Arcs named with the endpoints • Major Arcs and semicircles names with the endpoints and one point in-between. A Central Angle

  2. A D C B E • The measure of a minor arc is the measure of its central angle. • The measure of a major arc is 360 minus the degree of the central angle. • The measure of a semicircle = 180 AB = 150° BEA = 360° – 150° = 210° ABE = 180° = semicircle

  3. A D C B E AB = BE = ED = ABD = EDA = 135° 45° 135° 315° 180°

  4. Theorem 10-1 & Postulate 10-1 • Theorem 10-1: Two arcs are congruent if and only if their corresponding central angles are congruent. • Adjacent arcs are arcs that have exactly one point in common. • Postulate 10-1: The measure of an arc formed by adjacent arcs is the sum of the measure of two adjacent arcs. R Q If Q is a point on PR, then mPQ + mQR = mPQR C P

  5. D E C 48° A B Example • In Circle A, CE is a diameter. • Find mBC, mBE, and mBDE. • mBC = 48° • mBE = 132° • mBDE = 228°

  6. Arc Length • The length of an arc is part of the circumference, therefore it is equal to… A = degree measure of arc 360 = degree measure of whole circle l = arc length C = Circumference OR

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