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10-4 Inscribed Angles

10-4 Inscribed Angles. You found measures of interior angles of polygons. Find measures of inscribed angles. Find measures of angles of inscribed polygons. Find the measure of each arc. 54 ° 180° 306°. E. m DE m AED m EBD. 54 °. A. D. C. B. What kind of angle is angle ECD?

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10-4 Inscribed Angles

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  1. 10-4 Inscribed Angles You found measures of interior angles of polygons. • Find measures of inscribed angles. • Find measures of angles of inscribed polygons.

  2. Find the measure of each arc 54° 180° 306° E • mDE • mAED • mEBD 54° A D C B What kind of angle is angle ECD? Central angle

  3. B C A Definition His name was inscribed on the award. The square is inscribed in the circle. An inscribed angle is an angle with its vertex on a circle and sides that contain chords of the circle.

  4. Intercepted Arc An intercepted arc has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle R C Q Intercepted arc S P P P Center P is on a side of the inscribed angle Center P is inside the inscribed angle Center P is in the exterior of the inscribed angle

  5. Sizing Up Inscribed Angles A • Measure the central angle • What is the measure of the arc AB? • Measure the inscribed angle • Compare the measure of the central angle and the inscribed angle. C B D

  6. The measure of an inscribed angle is half the measure of its intercepted arc. A C B p. 723

  7. p. 724

  8. Find the measure of each angle or arc indicated by a variable. x° C 24° z° 160° 48° 90° y° 80°

  9. A. Find mX. Answer:mX = 43

  10. B. = 2(52) or 104

  11. A. Find mC. A. 47 B. 54 C. 94 D. 188

  12. A D If two inscribed angles intercept the same arc, then they are congruent. B C p. 724

  13. RS R and S both intercept . ALGEBRA Find mR. mRmS Definition of congruent angles 12x – 13 = 9x + 2 Substitution x = 5 Simplify. Answer:So, mR = 12(5) – 13 or 47.

  14. ALGEBRA Find mI. A. 4 B. 25 C. 41 D. 49

  15. An inscribed angle that intercepts a semicircle is a right angle. p. 725

  16. ALGEBRA Find mB. ΔABC is a right triangle because C inscribes a semicircle. mA + mB + mC = 180Angle Sum Theorem (x + 4) + (8x – 4) + 90 = 180 Substitution 9x + 90 = 180 Simplify. 9x = 90 Subtract 90 from each side. x = 10 Divide each side by 9. Answer:So, mB = 8(10) – 4 or 76.

  17. 10-4 Assignment Page 727, 11-18, 23-24

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