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## Warm up

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**Central Angle**Angle = Arc**Inscribed Angle**• Angle where the vertex in ON the circle**160**The arc is twice as big as the angle!! 80**Find the value of x and y.**120 x y **J**K Q S M Examples 1. If mJK= 80 and JMK = 2x – 4, find x. x = 22 2. If mMKS = 56, find m MS. 112 **Find the measure of DOG and DIG**D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I**If all the vertices of a polygon touch the edge of the**circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.**Quadrilateral inscribed in a circle: opposite angles are**SUPPLEMENTARY B A D C**If a right triangle is inscribed in a circle then the**hypotenuse is the diameter of the circle. diameter**Q**D 3 J T 4 U Example 3 In J, m3 = 5x and m4 = 2x + 9. Find the value of x. x = 3**Example 4**In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G Bonus: What type of triangle is this? Why?**Example 5 Find y and z.**z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95**Homework WS**Inscribed Angles Choose even or odd. Everyone does the last problem.