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10.2 Measuring Arcs and Angles Then: You measured angles and identified congruent angles. Now: 1. Identify central angles, major arcs, minor arcs, semicircles and find their measures. 2. Find arc lengths. https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQoQbm- Central Angle *Angle whose vertex is the center of a circle and whose sides are radii. *Sum of measures of the central angles of a circle with no interior points in common is 360. Example 1: Find Measures of Central Angles a. Find the value of x. 1. 2. Example 1: b. Find the value of x. Arcs of a Circle *Portion of a circle defined by two endpoints. Measure of: Minor arc- less than 180 and equal to the measure of its central angle. Major arc- greater than 180; Equal to 360 minus measure of the minor arc. Semicircle= 180 Example 2: Classify Arcs and Find Arc Measures 𝐵𝐷 and 𝐴𝐶 are diameters of Circle O. Identify each arc as a major arc, minor arc or semicircle of the circle. Then find its measure. a. m𝐵𝐴 b. m𝐵𝐶 c. m𝐶𝐷 Example 2 d. m𝐴𝐶𝐵 e. m𝐵𝐶𝐷 f. m𝐴𝐷 Congruent Arcs Example 3: Find Arc Measures in Circle Graphs Use the Bicycles Bought circle graph to find: a. m𝐾𝐿 b. m𝑁𝐽𝐿 Adjacent Arcs *Arcs in a circle that have exactly one point in common. http://ef004.k12.sd.us/ch10no1.gif Example 4: Use Arc Addition to Find Measures of Arcs Find each measure in Circle M. a. m𝐿𝐼 b. m𝐼𝐾 Arc Length *Distance between the endpoints along an arc measured in linear units. *Part of the circumference of a circle. Formula: Length of arc (l) = Measure of arc (x) 2r 360 𝑥 or l = 2r 360 Example 5: Find Arc Length a. Find length of 𝐴𝐵 to the nearest hundredth. Example 5 b. Use Circle O to find the length of each arc. Round to the nearest hundredth. 1. 𝐷𝐸 if r = 2 m 2. 𝐷𝐸𝐴 if d = 7 in Example 5 3. 𝐵𝐶 if BE = 24 ft 4. 𝐶𝐴 if DO = 3 mm Example 5 c. Find m𝐴𝐶 of Circle B. AB = 5.0 cm 𝐴𝐶 = 9.7 cm B C A Example 5 d. Find the radius of Circle B. A 𝐴𝐷𝐶 = 14.7 ft m𝐴𝐷𝐶 = 247 D B C Example 5 e. Find the circumference of Circle B. m𝐴𝐶 = 80 𝐴𝐶= 5.4 mm C B A 10.2 Assignment Pages 710-712 #12-42 evens, 43-50 all Show your work!!!