Transcript 6.4---inscribed-angles

For each circle C, find the value of x. Assume that segments that appear to be
tangent are tangent.
1)
2)
Math II
UNIT QUESTION: What special
properties are found with the parts of
a circle?
Standard: MM2G1, MM2G2
Today’s Question:
What is the relationship of an
inscribed angle to the measure of its
intercepted arc?
Standard: MM2G3.b
Inscribed Angle:
An angle whose
vertex
is on
the circle and
sides
are chords
whose
the circle
of
Determine whether each angle is an
inscribed angle. Name the intercepted
arc for the angle.
1.
C
T
O
L
YES;
CL
Determine whether each angle is an
inscribed angle. Name the intercepted
arc for the angle.
2.
Q

NO;
QVR
V
K

R

S
To find the measure of an inscribed angle…
Intercepted Arc
Inscribed Angle 
2
1600
800
What
do
we
call
this
type
angle?
WhatWhat
do
How
weis
do
call
the
we
this
solve
value
type
for
ofof
of
x?
y?
angle?
The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
120
x
y
Examples
3. If m JK = 80, find m <JMK.
40 
4. 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.
72
Example 5
In J, m<3 = 5x and m<4 = 2x + 9.
Find the value of x.
Q
D
x=3
T
3
J
4
U
If all the vertices of a polygon
touch the edge of the circle, the
polygon is INSCRIBED and the
circle is CIRCUMSCRIBED.
A circle can be circumscribed around
a quadrilateral if and only if its
opposite angles are supplementary.
B
A
D
C
mA  mC  180
mB  mD  180
Example 8 Find y and z.
z
110
110 + y =180
y
y = 70
z + 85 = 180
z = 95
85
If a right
triangle is
inscribed in a
circle then the
hypotenuse is
the diameter of
the circle.
180
Example 6
In K, m<GNH = 4x – 14. Find the value of x.
4x – 14 = 90
x = 26
H
K
G
N
Example 7
In K, m<1 = 6x – 5 and m<2 = 3x – 4. Find the
value of x.
6x – 5 + 3x – 4 + 90 = 180
or
K
6x – 5 + 3x – 4 = 90
G
x = 11
1
2
H
N