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- 1. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 14-1Inscribed Angles
- 2. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Inscribed Angle: An angle whose vertex is on the circle. INSCRIBED ANGLE INTERCEPTED ARC
- 3. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Name the intercepted arc for the angle. • C L O T 1. CL
- 4. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Name the intercepted arc for the angle. • Q R K V 2. QVR S • • • •
- 5. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 2 ArcdIntercepte AngleInscribed = 160º 80º To find the measure of an inscribed angle…
- 6. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 120 x What do we call this type of angle? What is the value of x? y How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!!
- 7. 120 x What is the value of x? y How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!! Since we know that the measure of x AND the measure of y must both equal half of 120, then we know that x=y 120/2 = 60 X= 60 Y= 60
- 8. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Examples 3. If m JK = 80°, find m ∠JMK. • M Q K S J 4. If m ∠MKS = 56°, find m MS. 40 ° 112 °
- 9. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 72º If two inscribed angles intercept the same arc, then they are congruent. Therefore we can say that the blue angle and the red angle have the same angle measurement
- 10. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4Find m∠ 4 Find arc QD Find arc QTD
- 11. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4 Since we know that angle 3 and 4 intersect the same arc, we know that they must be congruent, so we can set them equal to one another to find x. TRY IT!
- 12. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles Example 5 In J, m∠3 = 5x and m∠ 4 = 2x + 9. Find the value of x. 3 • Q D JT U 4
- 13. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles 180º d ia m eter If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
- 14. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles • H K G N 4x – 14 = 90 Example 6 GH is a diameter and m∠GNH = 4x – 14. Find the value of x. x = 26
- 15. Using Inscribed Angles & Polygons; Justifying Measurements & Relationships in Circles • H K G N 6x – 5 + 3x – 4 = 90 Example 7 In K, m∠1 = 6x – 5 and m∠2 = 3x – 4. Find the value of x. x = 11 1 2

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