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Inscribed Angles

Inscribed Angles. Concept 54. inscribed angle – and angle with a vertex on the circle and its sides are chords of the circle. Ex: intercepted arc – has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle . Ex:. A. P. C. B. Vocabulary. Concept.

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Inscribed Angles

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  1. Inscribed Angles Concept 54

  2. inscribed angle – and angle with a vertex on the circle and its sides are chords of the circle. • Ex: • intercepted arc – has endpoints on the sides of an inscribed angle and lies in the interior of the inscribed angle. • Ex: A P C B Vocabulary

  3. Concept

  4. Use Inscribed Angles to Find Measures 1. Find mX. Answer:mX = 43 Example 1

  5. 2. Use Inscribed Angles to Find Measures = 2(52) or 104 Example 1

  6. 3. Find mC. A. 47 B. 54 C. 94 D. 188 Example 1

  7. 4. A. 47 B. 64 C. 94 D. 96 Example 1

  8. Concept

  9. RS R and S both intercept . Use Inscribed Angles to Find Measures 5. 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. Example 2

  10. 6. ALGEBRA Find mI. A. 4 B. 25 C. 41 D. 49 Example 2

  11. Concept

  12. Find Angle Measures in Inscribed Triangles 7. 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. Example 4

  13. 8. ALGEBRA Find mD. A. 8 B. 16 C. 22 D. 28 Example 4

  14. Concept

  15. Find Angle Measures 9. INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT. Since TSUV is inscribed in a circle, opposite angles are supplementary. mS + mV = 180 mS + 90= 180 mS = 90 mU + mT = 180 (14x) + (8x + 4) = 180 22x + 4 = 180 22x = 176 x = 8 Answer:So, mS = 90 and mT = 8(8) + 4 or 68. Example 5

  16. 10. An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mN. A. 48 B. 36 C. 32 D. 28 Example 5

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