Warm up 30 80 100 180 100 260
- Slides: 16
Warm up 30 80 100 180 100 260
Inscribed Angles and Inscribed Quadrilaterals
Wheel of Formulas!!
Central Angle = Arc
Inscribed Angle • Angle where the vertex is ON the circle
Inscribed Angle
160 80 The arc is twice as big as the angle!!
Find the value of x and y. 120 x y = 120 = 60
Examples 1. If m. JK = 80 and JMK = 2 x – 4, find x. x = 22 2. If m MKS = 56 , find m MS. 112 J K Q M S
Find the measure of DOG and DIG 72˚ D If two inscribed angles O intercept the same arc, then they are congruent. G 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 A D B C
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. am di r e et
Example 3 In J, m 3 = 5 x and m 4 = 2 x + 9. Q Find the value of x. 5 x = 2 x + 9 3 x = + 9 x= D T 3 J 4 U
Example 4 In K, GH is a diameter and m GNH = 4 x – 14. Find the value of x. 4 x – 14 = 90 4 x = 104 G x = 26 H K N
Example 5 Solve for x and z. 2 x +18 + 22 x – 6 = 180 24 x +12 = 180 24 x = 168 x=7 z + 85 = 180 z = 95 z 2 x + 18 22 x – 6 85
