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Find the missing measures:

Warm up. Find the missing measures:. 130 °. D. A. R. 50. 120 °. 60. C. 230 °. B. Inscribed Angle : An angle whose vertex is on the circle and whose sides are chords of the circle. INTERCEPTED ARC. INSCRIBED ANGLE. YES; CL. C. T. O. L.

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Find the missing measures:

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  1. Warm up Find the missing measures: 130° D A R 50 120° 60 C 230° B

  2. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INTERCEPTEDARC INSCRIBEDANGLE

  3. YES; CL C T O L Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1.

  4. NO; QVR Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 2. Q V K R S

  5. To find the measure of an inscribed angle,divide the intercepted arc by 2… 160º 80º

  6. To find the measure of an intercepted arc,multiply the inscribed angle by 2… 160º 80º

  7. Ex. 1 Find m1. A B 1 124° C m1 = 62º

  8. Central Angle Inscribed Angle What is the value of y? What is the value of x? What do we call this type of angle? What do we call this type of angle? 60° 120° 120 x y

  9. J K Q S M Examples 3. If m JK = 80, find m JMK. 40  4. If m MKS = 56, find m MS. 112 

  10. If two inscribed angles intercept the same arc, then they are congruent. 72º A F B C

  11. Q D 3 J T 4 U Example: In J, m3 = 5x and m 4 = 2x + 9. Find the value of x. 5x = 2x+9 3x = 9 x = 3

  12. If all the vertices of a polygon touch the edge of the circle, then the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

  13. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

  14. Example: Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95

  15. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle AND the angle opposite the diameter is a right angle. 180º diameter

  16. Example: In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H 4x = 104 K x = 26 N G HINT: GH is also the __________ . Therefore, angle GNH is a ______ angle. hypotenuse right

  17. Example 7 Kis a right triangle.In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x. 6x – 5 + 3x – 4 = 90 H 9x – 9 = 90 2 K 9x = 99 N 1 x = 11 G HINT: Angle GNH is a ________ angle. Therefore, angles G & H are __________ . right complementary

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