Quadrilaterals Quadrilaterals: A Review Game Moody Mathematics.
Warm up 30 80 100 180 100 260 . Inscribed Angles and Inscribed Quadrilaterals.
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Transcript of Warm up 30 80 100 180 100 260 . Inscribed Angles and Inscribed Quadrilaterals.
Warm up3080100180
100260
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
160
80
The arc is twice as big as the angle!!
ARCANGLE =
2
Inscribed angles
120
x
y
Find the value of x and y.
= 120
= 60
Examples1. If mJK = 80 and JMK = 2x – 4, find x.
M
Q
K
S
J
2. If mMKS = 56, find m MS.
x = 22
112
If two inscribed angles intercept the same arc, then they are
congruent.
BAD =BCD
A
B
C
D
Find the measure of DOG ,DIG, ODI and OGI
D
O
G
I
102
74
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, m3 = 5x and m 4 = 2x + 9.Find the value of x.
3
Q
D
JT
U
4
5x = 2x + 9
x = 3
3x = + 9
4x – 14 = 90
H
K
GN
Example 4
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
x = 26
4x = 104
z
2x + 18
85
2x +18 + 22x – 6 = 180
x = 7
z + 85 = 180z = 95
Example 5 Solve for x and z.
22x – 6 24x +12 = 18024x = 168
Textbook
p. 420#2 – 13 (omit
#6), 17 – 20, 22