Euclidean Geometry
Section 10.4
Name: __Key__________________
Angles formed by chords, tangents and secants Date: _________________
I. Find the measure of each indicated arc or angle. When point O is shown, it is
the center of the circle. You may assume that segments that look like tangents
are tangents.
1.
2.
3.
2100
800
1
2 1
400
1
600
1000
m1  _ 300 __
m1  _1050
m1  _ 700 _
m2  _1100
4.
2800
5.
6.
440
O
O
1
640
1
1120
1
m1  _ 400 _
m1  _ 580 _
7.
8.
m1  _ 560 _
1
1000 1
A
9.
980
O
1040
770
860
m1  _ 800 _
10.
B
m1  _ 880 _
mAB  _1540
11.
B
12.
0
172
A
750
A
1
B
650
320 O
1160
T
mAB  _ 640 _
mATS  _1220
S
m1  _ 500 _
D
C
mDC  _ 550 _
II. In exercises 1 – 4, AB and CD are chords.
1. If mAC  850 and mDB  730 , then m1  _ 790 _ .
A
D
2. If mAD  136 and mCB  96 , then m1  _ 64 _ .
0
0
0
1
3. If m1  54 and mAC  78 , then mDB  _ 30 _ .
0
0
0
C
4. If m1  480 and mDB  420 , then mAC  _ 540 _ .
B
Exs. 1 - 4
In exercises 5 – 7, EF and EG are tangents.
5. If mFHG  2800 , then mE  _1000 .
6. If mFG  960 , then mE  _ 840 _ .
F
H
E
7. If mE  90 , then mFHG  _ 270 .
0
0
Exs. 5 - 7
G
In exercises 8 – 10, IJ is a tangent.
8. If mJK  1200 and mJL  400 , then mI  _ 400 _ .
L
9. If mI  450 and mJL  550 , then mJK  _1450 .I
K
10. If mI  500 and mJK  1100 , then mJL  _100 _ .
J
Exs. 8 - 10
In exercises 11 – 15, RP and RT are secants.
11. If mPT  1000 and mQS  200 , then mR  _ 400 _ .
P
12. If mPT  130 and mQS  40 , then mR  _ 45 _ .
0
0
0
Q
R
13. If mR  250 and mQS  250 , then mPT  _ 750 _ .
S
14. If mR  400 and mPT  1300 , then mQS  _ 500 _ .
T
Exs. 11 - 15
15. If mST  900 , mQS  600 , and mQP  800 , then mR  _ 350 _ .
III. Find the value of x.
1. 800
2.
500
x
x0
700
800 3.
4.
x0
0
1250 x
1000
200
5.
1600
12001400
6.
2300
400
1400
x
0
7.
0
8.
35
300
800
x
0
100 0
0
x
300
800
500
x0
Euclidean Geometry
1200
1000
1500
Section 10.4
Key
p. 2