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10-2 Measuring Angles and Arcs

10-2 Measuring Angles and Arcs. You measured angles and identified congruent angles. Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. Find arc lengths. Central angles. Central angles are angles whose vertices are at the center of the circle.

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10-2 Measuring Angles and Arcs

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  1. 10-2 Measuring Angles and Arcs You measured angles and identified congruent angles. • Identify central angles, major arcs, minor arcs, and semicircles, and find their measures. • Find arc lengths.

  2. Central angles Central angles are angles whose vertices are at the center of the circle. Central angle p. 706

  3. The sum of the measures of Find Measures of Central Angles Find the value of x. Substitution Simplify. Add 2 to each side. Divide each side by 26. Answer: x = 7

  4. Minor arc AB Major arc ADB A C B D Arcs—parts of a circle There are three kinds of arcs made by central angles: Major arcs: greater than 180° Named with 3 letters Minor arcs: less than 180° Named with 2 letters Semi-circles: exactly 180° Named with 3 letters one-half of a circle A C B D

  5. Measures in Degrees • Complete circle measures 360°. • The measure of any semicircle is 180°. (½ of a circle) 360° 180° C A B

  6. p. 707

  7. Measures W • Measure of a minor arc is equal to the measure of the central angle. • Measure of the major arc is equal to 360° minus the measure of its minor arc. Y 80° X Z W mXZY = 360°−mWX 80° Y X Z

  8. Answer:

  9. Answer:

  10. Answer:

  11. Definition Congruent arcs are arcs in the same circle (or congruent circles) that have the same measure. A Y 60° 60° B X

  12. p. 707

  13. Answer: mLPK = 0.21(360) Find 21% of 360. = 75.6 Simplify.

  14. Answer: Sum of arcs in a circle is 360. Substitution Simplify. Simplify.

  15. A.124.3 B.140.4 C.155.6 D.165.9

  16. M L N Q Find each arc measure in סּL 54° 306° 180° • mMN • mMPN • mPQN 54° P

  17. 10-2Assignment Page 710, 12-24

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