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Warm up

Warm up. 30 . 8 0 . 100 . 180 . 100 . 260 . Wheel of Formulas!!. Central Angle. Angle = Arc. Inscribed Angle. Angle where the vertex is ON the circle. Inscribed Angle. 160 . The arc is twice as big as the angle!!. 80 . Find the value of x and y. 120 . . 120 . x.

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Warm up

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  1. Warm up 30 80 100 180 100 260

  2. Wheel of Formulas!!

  3. Central Angle Angle = Arc

  4. Inscribed Angle • Angle where the vertex is ON the circle

  5. Inscribed Angle

  6. 160 The arc is twice as big as the angle!! 80

  7. Find the value of x and y. 120  120 x  60 y 

  8. J K Q S M Examples 1. If mJK= 80 and JMK = 2x – 4, find x. x = 22 2. If mMKS= 56, find m MS. 112

  9. Find the measure of DOG and DIG D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I

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

  11. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY B A D C

  12. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

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

  14. Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G

  15. Example 5 Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95

  16. Practice WS 10 problems

  17. Homework WS 6.4 Practice

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