Warm up. Review HW. Inscribed Angle. Angle where the vertex in ON the circle. Inscribed Angle. 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 m JK = 80 and JMK = 2x – 4, find x. - PowerPoint PPT Presentation
Transcript of Warm up
Warm up
Review HW
Inscribed Angle
• Angle where the vertex in ON the circle
Inscribed Angle
ARCANGLE =
2
2
ArcdIntercepteAngleInscribed
160
80
The arc is twice as big as the angle!!
120
x
y
Find the value of x and y.
Examples1. If mJK = 80 and JMK = 2x – 4, find x.
M
Q
K
S
J
2. If m MKS = 56, find m MS.
x = 22
112
72˚
If two inscribed angles intercept the same arc, then they are congruent.
Find the measure of DOG and DIG D
O
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 B
CD
180 CmAm180 DmBm
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
diameter
Example 3
In J, m 3 = 5x and m 4 = 2x + 9.Find the value of x.
3
Q
D
JT
U
4
x = 3
4x – 14 = 90
H
K
GN
Example 4
In K, GH is a diameter and m GNH = 4x – 14. Find the value of x.