©N w2g07131s sKeuRtBau zSeowfct1wLaerweB 1LnLrCw.w b wA0lalL Drhi6gmhJt7sS nrOedsXeqrLvzeEdP.i W pMmaCdten fwPiLthhk 9ITnTftiunbittgeG EGIetormVe9tjr4yQ.A Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________Secant-Tangent and Tangent-Tangent Angles
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
1)
EF
G
?
76°2)
V
T
U
?
50°
3)
SR
Q
146°
?
4)
P
R
Q
120°
?
5)
M
L
K
130°
?
6)
S
R
P
Q
?
65°
44°
7)
J
L
K
110°
?
8)
K
L
N
M
129°
61°
?
Solve for
x
. Assume that lines which appear tangent are tangent.
9)
HG
E
F140°
48°
3
x
+ 13
10) T
V
U
110°
5
x
+ 10
-1-
©T W2A0w1G1Z kKUu6tJaO 5S8o7fttwwIaArAe3 sL1LzCz.p w ZAKlAlu Lr1i2gkhEtDsJ trIeFsveTr2vje2dc.y I yMUaedIep 4wBiqtMhP 8IKnQfYiBnRi3tceq 0GjeRovmCeAtbrvyC.G Worksheet by Kuta Software LLC
11)
P Q
S
R
190°
13
x
− 7
5
x
− 5
12)
FE
D
120°
7
x
− 10
13)
W U
V
37
x
+ 5
23
x
− 5
5
x
+ 17
14) C
B
A
38
x
+ 2
16
x
+ 4
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
15) Find mBD
B
D
C
−12 + 21
x
12
x
− 24
6
x
− 12
16) Find m∠DEG
D
E
G
F
6 + 14
x
58°
2
x
+ 14
17) mPSQ =
30
x
+ 6
Find mPSQ
R
Q
P
S
11
x
− 5
18) Find mNK
K
LN M
25
x
+ 3
9
x
+ 3
7
x
+ 6
-2-
©x g2G01121r DKeuwtMak FSkoCfWtPwoaorAeF uLfLFCr.f o OAmlDlH Vrqicg4hDtyse 7rfehsteYrNvze7dj.n t vMwabd5eN BwtihtGhp hIQnpfQiVnRiDtheQ AGneeoJm6entRrnyW.q Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________Secant-Tangent and Tangent-Tangent Angles
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
1)
EF
G
?
76°
208°
2)
V
T
U
?
50°
130°
3)
SR
Q
146°
?
73°
4)
P
R
Q
120°
?
60°
5)
M
L
K
130°
?
65°
6)
S
R
P
Q
?
65°
44°
153°
7)
J
L
K
110°
?
70°
8)
K
L
N
M
129°
61°
?
34°
Solve for
x
. Assume that lines which appear tangent are tangent.
9)
HG
E
F140°
48°
3
x
+ 13
11
10) T
V
U
110°
5
x
+ 10
12
-1-
©8 o2s0V1H1E pKfuYtYag 7SooBfqtNwAaArIeE vLwLXCt.P 2 YAClslF crCiBg4h9tcss YrLeKsXeZrtvke2dl.3 J LM5aXdZee Yw2iItAhT kIWn7ffienbiktge7 eGEecodmKeetFrIyx.Q Worksheet by Kuta Software LLC
11)
P Q
S
R
190°
13
x
− 7
5
x
− 5
9
12)
FE
D
120°
7
x
− 10
10
13)
W U
V
37
x
+ 5
23
x
− 5
5
x
+ 17
6
14) C
B
A
38
x
+ 2
16
x
+ 4
5
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
15) Find mBD
B
D
C
−12 + 21
x
12
x
− 24
6
x
− 12
120°
16) Find m∠DEG
D
E
G
F
6 + 14
x
58°
2
x
+ 14
30°
17) mPSQ =
30
x
+ 6
Find mPSQ
R
Q
P
S
11
x
− 5
216°
18) Find mNK
K
LN M
25
x
+ 3
9
x
+ 3
7
x
+ 6
153°
-2-
Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com
©1 Z2z0d1B1z QK3uKtNaJ nSNoAfBtywMalrKeZ 3L8LuCp.X o 0AWlvl3 GriiYghhQtws6 0rneLsneErgvZeZdO.X r vM6aSdGe7 Owbirt2hv sIcnEfRiVnwiwtXeW bGMelowm9e7tzr0yC.E Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________Segment Lengths in Circles
Solve for
x
. Assume that lines which appear tangent are tangent.
1) 15
9
x
2)
4
x
5
3
3) 4
x
− 3
x
− 65
4)
64
x
5)
9
4
x
4
x
+ 2
8
6)
5
8
x
4
7) 6
x
5
8) 8
x
6
x
97
-1-
©c D2S091A1K fKluatdaU 7ShoqfTtwwSaYrceO eLeLCCs.G z EASlnld Erdi1gxhItBsh 4rEeYsaeKrlv9eYdH.d d qMUa8dueO MwPiJtShA uIDngfiixnXiGtZeg KGCeIoUmXextSr9yB.l Worksheet by Kuta Software LLC
Find the measure of the line segment indicated. Assume that lines which appear tangent are tangent.
9) Find UW
14
2
x
+ 2
2
x
+ 5
12T
U
V
W
C
10) Find KM
3
2
x
+ 5
24
K
W
ML
N
11) Find NM
x
+ 3
x
− 3
16
N
K
M
L
12) Find NL
4
x
− 8
x
− 5
3
NS
L
M
K
13) Find CE
9
2
x
− 1710
8
C
S
E
DF
14) Find CA
12
4
x
+ 1
3 + 3
x
14
DC
B
A
L
15) Find HG
x
+ 8
12
15
H
E
G
F
16) Find WS
9
8
6
x
12
x
P
Q
R
S
W
-2-
©h o2A0A1K1v dKluKtpaZ sSFoafmtYwfaPrPeP 8L3LxCY.G G 5A6l5ly tryifghhgt3sk hrDeWsse1rPvEeHdC.y a KM9a6dle3 uwniatAha PI0nIf4iendiPtheC PGVeMoXm8entprDyo.X Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry Name___________________________________
Period____Date________________Segment Lengths in Circles
Solve for
x
. Assume that lines which appear tangent are tangent.
1) 15
9
x
16
2)
4
x
5
3
2
3) 4
x
− 3
x
− 65
9
4)
64
x
5
5)
9
4
x
4
x
+ 2
8
4
6)
5
8
x
4
10
7) 6
x
5
4
8) 8
x
6
x
97
1
-1-
©w e2p0A1G1O LKeuMtdaZ KSEoufZt1wBaorUep ULPLxCJ.8 p YA5lplC RrbiVgnhitfse erPews1ewr9vyeYdC.5 9 iM0acd1eG OwxihtOha mIRnofainnWiFt4ek PGDeVovmFezthrQyB.5 Worksheet by Kuta Software LLC
Find the measure of the line segment indicated. Assume that lines which appear tangent are tangent.
9) Find UW
14
2
x
+ 2
2
x
+ 5
12T
U
V
W
C
33
10) Find KM
3
2
x
+ 5
24
K
W
ML
N
8
11) Find NM
x
+ 3
x
− 3
16
N
K
M
L
15
12) Find NL
4
x
− 8
x
− 5
3
NS
L
M
K
6
13) Find CE
9
2
x
− 1710
8
C
S
E
DF
16 14) Find CA
12
4
x
+ 1
3 + 3
x
14
DC
B
A
L
32
15) Find HG
x
+ 8
12
15
H
E
G
F
18
16) Find WS
9
8
6
x
12
x
P
Q
R
S
W
6
-2-
Create your own worksheets like this one with Infinite Geometry. Free trial available at KutaSoftware.com
KuLa Soft van: - Inlillill Gl' 1111dr\'
SecaJlt-Tall~ellt anJ Tall!!ent-Tanl-!.enl i\11!.!.le_l..... '- ~,.
Hncl 1I1l' ll1('a~lIII'C or tbl: an' (If' 'lIl~ll· illdkalcd. "\SSllIIlC Ih•• '
?
7~': ±~f?
7'°:' ~ )<.
ISZ·~)(. ,. r
"O-ISl =l08°
,nLS2Q: ! (l~' t) fY' L5R.Q =- 73
o
rt\ LQ =~C1jb-ll0) (h L Q=- ~ (f20)
MLG=--'OQr ,I
~~o= i lX-'S) 88 0 : x-fo~
, 1 t5"3°:.x.
x:: 1(,1Q-C,I) '" ~ t (68)
'1- =- '3~ \)
I );II~ l'er10t!
Jim's "hich apprar llingt'nl arl.· langrnl.
I \
»t l3
lx +13= 1. (ND -I./W) 3xtt3= ~(ql)
))( t 13:. ~,
3~~ 33 ~~ t\
__
\I'
I
/' I
II!
sX-s -=- t&O -(,3x -7~ ('- - ¢'t!
! ' 5"'1--~ =. t (,QO -/3)( .... 7)
1.\ /
/' ~,~ l ID'I{ -/0 = (flO -13~ r 7
S
Z3y...:: zo 7 , J- \'_"or· ; ...' 'f.:=. q
!~ /' \,
5~~17 ~ ~ (37x-rS -(l3x-S))
( II
S~tI7:; i l37~t)-Z3x.-+S)
IOxtJ'f:: ILJ~ +/0 lV :: ~"(.
c,=x.
2'1.+'" = i (,+Jlf)C -S8) 4~ +l ~ ~ 0 t/Yj.-r8
~o =- /0)(. ~ =: 'f...
7'1- tb =- ~ (Zf~t3 -0)(+ 3)) lLf,,+-I~= l'~ +0
Ii ::. Zx.
&:~
Kula ll't-.,v'lr',... I11 (" ,, - 1Il1lt' (, 'illlldry · a1TI-:-------
Segm H1 Lel1gth~ in Circles [);Il~____ I'eri ld_
Sol\'(.' for r , ,~ ~llml' lhat lil1t.'~ \\ bil-II . .. ..t) • 4 <lPI'(,1I tangellt art lallgl'lIL
-)
~('ttC/)= egO)
~'t. t"::: 2'1
Lf)<. ~ "i qlx~q) == IS 2 'f.:=- L q'ltRt= zzr
1¥- =- 14~
~-=-J'
)<-3
)( -b '
4(Xf'l) =~ Z Y(~-3 +V):: )(X-b +~-)
~~ 1-1' =Sb~(>, +1) ~ ){)\. -I)
~y.. -=- Zu ~'1.. tY :: 5" ~ -~ y.:=-~
9 ::: K
_ 1 A~
x
II) Find .\'.<H
I zt3
®
I.) iIllI J-J(;
fIt C-l _------ Ie
, -. ·-\..V )(t~ ,'/
(Qf1
®
~C X-+5J ~ ,1~ Z +5~.:: 3" '"L +$")( - 3':: 0
(y. t q '{'k -t1 ):: 0
'1--3(~~3 .}/b) ::~+ 5)"(
~ __ s( ~ + 13) :::. "'-Z. ~'X +q
'( 1. +10)(.. _ s1 ::: y... 7.. t'x. +'f LJ K = 4X
,,-=..tZ
IZ .l7.:: ~+ g)l
32'1 =- ~ t }J' ~ t6J If ~ '( +Jb~ -l~o::. 0
('><+"lG.J(lI:-lO) .:0
)( ~7(, cr 1-.. =- J ()