1 / 17

Angles and Arcs

Angles and Arcs. Section 10-2. Central Angle:. A central angle is 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 °. Arc.

mahala
Download Presentation

Angles and Arcs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Angles and Arcs Section 10-2

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

  10. 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

  11. 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

  12. 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

  13. 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

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

  15. Lesson Quiz: Part I 1. The circle graph shows the types of cuisine available in a city. Find the length of TRQ and the area of the sector bounded by TRQ if the diameter of the circle is 16. 158.4

More Related