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Notes 10-2

Learn about central angles, arcs, congruent arcs, adjacent arcs, arc length, and sector area in circles. Practice calculating angles and finding lengths and areas of arcs and sectors.

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Notes 10-2

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  1. Notes 10-2 Angles and Arcs

  2. Central Angle: • A central angleis an angle whose vertex is the center of a circle. • Sides are two radii of the circle. • The sum of the measures of the central angles of a circle is 360°.

  3. Arc • An arcis an unbroken part of a circle created by the sides of a central angle. • The measure of an arc is = to the measure of its corresponding central angle. • Congruent Arcs have the same measure.

  4. mKLF = 360° – 126° Example: The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF. = 234

  5. Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.

  6. Find mBD. mBD = mBC + mCD Example: = 97.4 + 30.6 = 128

  7. mJKL mKL = 115° mJKL = mJK + mKL Check It Out! Example 2a Find each measure. mKPL = 180° – (40 + 25)° Arc Add. Post. = 25° + 115° Substitute. = 140° Simplify.

  8. mLJN mLJN = 360° – (40 + 25)° Check It Out! Example 2b Find each measure. = 295°

  9. Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find mTRQ. 158.4

  10. Length of an Arc • The length of an arc is a fraction of the circumference of the circle.

  11. Example: Finding Arc Length Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. FG  5.96 cm  18.71 cm

  12. Example 4B: Finding Arc Length Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. an arc with measure 62 in a circle with radius 2 m  0.69 m  2.16 m

  13. Example: Find each arc length. Give your answer in terms of and rounded to the nearest hundredth. an arc with measure 135° in a circle with radius 4 cm = 3 cm  9.42 cm

  14. Sector – Region of a circle bounded by a central angle and its arc. Sector angle is related to the angle measure of the entire circle (360). The area of a sector is a part of the area of the circle. Sector

  15. Example: • Area of a sector = ? • Find the area of the sector that contains 46 degrees.

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