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Geometry
9.6
Interior and Exterior Angles
Interior Angle Theorem
The measure of an angle formed by two chords
that intersect inside a circle is equal to half the
sum of the measures of the intercepted arcs.
A
1
50˚
D
B
60˚
m<1 = ½( mAD + mBC )
C
If mAD = 50 and mBC = 60
55
m<1 = ½(50 + 60) = _____
Let’s try some exercises!
(which wonderful student can draw some pictures on the board?)
x
80
X
O
O
20
Find the value of x.
1.
50
x = _____
100
90 = ½(100 + x)
80
2. x = _____
Try these!
70
x
O
140
160
Find the value of x.
120
3. x = _____
O
Be careful:
Notice which angle x is
125
4. x = _____
x
40
Exterior Angle Theorem
(this is not in your packet)
The measure of the angles formed by intersecting
secants and tangents outside a circle is equal to half the
difference of the measures of the intercepted arcs.
x˚
y˚
m<1 = ½(x – y)
1
x˚
x˚
y˚
y˚
2
m<3 = ½(x – y)
m<2 = ½(x – y)
3
Let’s try some exercises!
230
A
150
O
O
B
130
x
x
35
Find the value of x.
1.
50
x = _____
35 = ½(150-x)
80
2. x = _____
Don’t forget about the ½
Let’s do these!
80
180
140
O
120
x
O
30
100
50
Find the value of x.
30
3. x = _____
10
4. x = _____
Don’t forget about the ½
x
Try the next four.
40
x
105
85
O
O
x
85 = ½(105 + x)
Find the value of x.
1.
65
x = _____
40 = ½[(360-x) – x]
40 = ½[360 – 2x]
80 = 360 – 2x
2x = 280
140
2. x = _____
More Problems
x
20
x
O
55
80
120
O
160
Find the value of x.
15
3. x = _____
40
4. x = _____
Find the measure of each numbered angle.
We can put the screen up and write on the picture.
B
A
125
●
8
7
3
100
C
O
●
2 1
6
30
E
25
5
F
4
80
G
D
AB is a tangent
mAG = 100
mCE = 30
mEF = 25
80
m<1 = ____
62.5
m<5 = ____
100
m<2 = ____
35
m<6 = ____
27.5
m<3 = ____
90
m<7 = ____
117.5
m<4 = ____
62.5
m<8 = ____
Homework
pg. 358 CE #1-9
WE # 1-23