1. GEOMETRY HELP Because there are 360° in a circle, multiply each percent by 360 to find the measure of each central angle. 65+ : 25% of 360 = 0.25 360 = 90 45–64: 40% of 260 = 0.4 360 = 144 25–44: 27% of 360 = 0.27 360 = 97.2 Under 25: 8% of 360 = 0.08 360 = 28.8 A researcher surveyed 2000 members of a club to find their ages. The graph shows the survey results. Find the measure of each central angle in the circle graph. Quick Check Circles and Arcs LESSON 10-6 Additional Examples

2. GEOMETRY HELP. Identify the minor arcs, major arcs, and semicircles in P with point A as an endpoint. Minor arcs are smaller than semicircles. Two minor arcs in the diagram have point A as an endpoint, AD and AE. Major arcs are larger than semicircles. Two major arcs in the diagram have point A as an endpoint, ADE and AED. Two semicircles in the diagram have point A as an endpoint, ADB and AEB. Circles and Arcs LESSON 10-6 Additional Examples Quick Check

3. GEOMETRY HELP mDXM = 56 + 180Substitute. mDXM = 236Simplify. mXY = mXD + mDYArc Addition Postulate mXY = m XCD + mDYThe measure of a minor arc is the measure of its corresponding central angle. mXY = 56 + 40Substitute. mXY = 96Simplify. Find mXY and mDXM in C.. mDXM = mDX + mXWMArc Addition Postulate Circles and Arcs LESSON 10-6 Additional Examples Quick Check

4. GEOMETRY HELP C = dFormula for the circumference of a circle C = (24)Substitute. A circular swimming pool with a 16-ft diameter will be enclosed in a circular fence 4 ft from the pool. What length of fencing material is needed? Round your answer to the nearest whole number. The pool and the fence are concentric circles. The diameter of the pool is 16 ft, so the diameter of the fence is 16 + 4 + 4 = 24 ft. Use the formula for the circumference of a circle to find the length of fencing material needed. About 75 ft of fencing material is needed. Draw a diagram of the situation. C 3.14(24)Use 3.14 to approximate. C 75.36Simplify. Circles and Arcs LESSON 10-6 Additional Examples Quick Check

5. GEOMETRY HELP length of ADB = 2 (18)Substitute. 210 360 The length of ADB is 21 cm. Find the length of ADB in M in terms of.. length of ADB = 21 mADB 360 length of ADB = 2 rArc Length Formula Because mAB = 150, mADB = 360 – 150 = 210.Arc Addition Postulate Circles and Arcs LESSON 10-6 Additional Examples Quick Check