Notes 10-2 Angles and Arcs

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 An arc is 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.

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

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

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

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

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

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

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

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

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

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

Sector 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.

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