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Transcript 
Warm up
30
80
100
180
100
260
Inscribed Angles
and Inscribed
Quadrilaterals
Central Angle
Central Angle = Arc
Inscribed Angle
•Angle where the vertex is
ON the circle
Inscribed Angle
Inscribed Angle = intercepted Arc/2
ARC
ANGLE =
2
160

80
The arc is twice as
big as the angle!!
Inscribed angles
Find the value of x and y.
120

x
y=

= 120
60
Examples
1. If mJK = 80 and JMK = 2x – 4, find x.
x = 22
2. If mMKS = 56, find m MS.
112 
J
K
Q
M
S
If two inscribed angles intercept the
same arc, then they are congruent.
A
C
B
BAD =BCD
D
Find the measure of DOG ,DIG,
ODI and OGI
D
74
G
O
102
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
mA  mC  180
mB  mD  180
If a right triangle is inscribed in a
circle then the hypotenuse is the
diameter of the circle.
Example 3
In J, m3 = 5x and m 4 = 2x + 9.
Find the value of x.
5x = 2x + 9
3x = + 9
x=3
Q
D
T
3
J
4
U
Example 4
In K, GH is a diameter and mGNH = 4x – 14.
Find the value of x.
4x – 14 = 90
4x = 104
G
x = 26
H
K
N
Example 5 Solve for x
and z.
2x +18 + 22x – 6 = 180
24x +12 = 180
24x = 168
x=7
z + 85 = 180
z = 95
z
2x + 18
22x – 6
85
Textbook
p. 420
#2 – 13 (omit #6),
17 – 20, 22
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