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Understanding Central Angles and Arc Measures in Circles

This guide covers the fundamentals of central angles and arc measures in circles, focusing on the definitions of major and minor arcs, as well as semicircles. You'll learn how to name angles and arcs using letter notation, understand the relationship between a central angle and its corresponding arc, and apply the Arc Addition Postulate with practice problems. Key concepts include measuring arcs, naming conventions, and the property that vertical angles are equal. Ideal for students looking to reinforce their knowledge of circle geometry.

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Understanding Central Angles and Arc Measures in Circles

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  1. Find Arc Measures

  2. Central Angle : An Angle whose vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P To name: use 3 letters C To name: use 2 letters B APB is a Central Angle

  3. EDF Semicircle: An Arc that equals 180° To name: use 3 letters E D P F

  4. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal A D B C

  5. measure of an arc = measure of central angle m AB m ACB m AE • EQA is a central angle. IfÐEQAis 80° then EA = 80° A E = 96° 96 Q B 264° = C 84° =

  6. Arc Addition Postulate m ABC = m AB + m BC A Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. C B

  7. m DAB = Tell me the measure of the following arcs. 240 D A 140 260 m BCA = R 40 100 80 C B

  8. P 6 12 R P R Q Q

  9. Practice!! page 193 (2-8 evens, 9-23 all)

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