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.