Download 11-Arcs and Central Angles

Kuta Software - Infinite Geometry
Name___________________________________
Arcs and Central Angles
Date________________ Period____
Name the arc made by the given angle.
2) ∠1
1) ∠FQE
I
F
H
1
Q
J
E
D
Name the central angle of the given arc.
3) ML
4) ML
L
L
M
K
1
Q
M
K
If an angle is given, name the arc it makes. If an arc is given, name its central angle.
5) RS
6) Major arc for ∠1
B
T
C
Q
2
1 3
S
R
A
7) ∠KQL
8) SVT
J
V
R
U
K
Q
T
Q
L
I
S
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters
are actual diameters.
9)
10)
155°
?
123°
?
Page1
120°
©P j260r1w2d 8Kfukt5a8 rSMoofqtcwxaJr1eI fLELOCD.J N AAqlWl6 jrOi6gDhwtRsb QrreussePravferdm.n r tMNazdhet 9wKi7t6hl wI2nOfvi1nIiptseF BGFejoLmteztjr8yE.S
-1-
Worksheet by Kuta Software LLC
11) mCFD
12) m∠SPQ
E
Q
154°
F
86°
D
81°
P
135°
U
R
C
T
60°
S
B
14) m∠MIJ
13) mEFC
C
B
K
I
E
126°
55°
J
D
F
M
L
Solve for x. Assume that lines which appear to be diameters are actual diameters.
15)
16)
x + 93
140°
6x − 8
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters
are actual diameters.
18) m∠VST
17) mWV
−37 x + 2
W
T
V
12 x − 2
S
U
5 x + 10
U
S
V
T
©r F2n0R1o2g aKyuet3aA NSvoZfct6wzatrOee tL2LbCY.M J MAClYl0 ermiugehctdsc crHeAsae5ryv0ejdh.7 S 0MBa0dyeO jwfiPt7hZ NIunBfWienTi7tseu uGle6oOmueUt9rNyo.U
−27 x − 3
Page2
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry
Name___________________________________
Inscribed Angles
Date________________ Period____
State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.
1)
2)
C
L
B
M
K
A
3)
4)
X
K
L
V
M
W
Find the measure of the arc or angle indicated.
5)
6)
C
80°
X
42°
B
?
7)
V
W
A
?
8)
E
D
?
49°
35°
F
70°
D
P
?
©x k260S1b2I 1KGu7tpaD kSPovfft2w3a3r0eS 2LwLICJ.s V zA9l0lu PrXiMgwhUtRsI dryeos7eErcvNepd0.I Y oMxaidreS qw5ietdhA eIAntfvi7nIiHt5eZ 2Gaeooim1evtrrzyo.6
C
B
Page3
-1-
Worksheet by Kuta Software LLC
9)
10)
G
75°
R
S
F
95°
?
168°
?
119°
V
65°
Q
H
Solve for x.
11)
12)
K
F
50°
110°
G
P
31 x + 3
R
30 x
192°
E
Q
Find the measure of the arc or angle indicated.
13) Find m∠NLM
14) Find mFGH
L
G
13 x − 10
21 x − 2
H
M
F
38 x + 5
A
7 x − 10
N
Solve for x and y.
15)
16)
L
L
10 x
X
4 + 18 y
10 x − 6
7x + 1
M
6 x − 10
V
16 y + 6
2 y + 100
2 y + 74
N
©S X2h0F1F2Q hKMu8tbad oSJokflthwMalrseY BLFL9C1.m D 9A6lMlV HraiVgJhdtAsp Pr0epsJeOrnvFeWdC.c A oMXaldleX SwLi8tchS tIWnqf7ignciWtMei tGvezocmLektirsyh.7
M
N
Page4
-2-
Worksheet by Kuta Software LLC
Name
Class
Date
Practice 11-3
Inscribed Angles
For each diagram, indicate a pair of congruent inscribed angles.
A
1.
2.
B
3.
A
A
B
O
D
C
D
B
C
E
C
D
Find the value of each variable.
4.
5.
90!
x!
y!
x!
z!
110!
8.
x!
35!
x!
170!
7.
6.
y!
9.
220!
240!
O
28!
x!
10.
11.
y!
z!
50!
z!
x!
12.
54!
x!
70!
y!
y!
y!
z!
x!
100!
C
z!
x!
Find each indicated measure for !O.
0
13. a. mAE
10!
b. m"C
A
14. a. m"A
20!
C
B
A
B
b. m"B
c. m"BEC
c. m"C
d. m"D
d. m"D
100!
120!
O
O
D
D
60!
C
E
Page5
4
Lesson 11-3 Practice
Geometry Chapter 11
© Pearson Education, Inc. All rights reserved.
62!
Kuta Software - Infinite Geometry
Name___________________________________
Secant-Tangent and Tangent-Tangent Angles
Date________________ Period____
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
1)
2)
U
76°
F
50°
E
T
?
?
V
G
3)
4)
Q
Q
?
146°
R
120°
P
S
R
?
5)
6)
R
44°
Q
K
65°
130°
S
L
M
?
P
7)
?
8)
L
L
M
110°
J
?
61°
K
K
N
?
©x E2a0A1t2S SKuuGt9ag lSPoQfhtDw9adrPeU TL2LCCO.f T UAMlhlK drGidg9hxtlsi Wr4e5snevrrvjeYde.k T wMwaZdyek uwQiptzhx cI4n3fZiPnYi9tbeI 4GoeeoymneRtSroyZ.P
129°
Page6
-1-
Worksheet by Kuta Software LLC
Solve for x. Assume that lines which appear tangent are tangent.
9)
10)
E
T
5 x + 10
110°
140°
48°
U
F
G
H
V
3 x + 13
11)
12)
5x − 5
P
7 x − 10
E
Q
F
13 x − 7
190°
120°
R
D
S
13)
14)
V
5 x + 17
C
16 x + 4
B
W
23 x − 5
A
U
38 x + 2
37 x + 5
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
16) Find m∠DEG
15) Find mBD
E
C
D
6 x − 12
2 x + 14
F
12 x − 24
58°
D
B
−12 + 21 x
©2 Y2B0Z1r2C bKeuDtPaU oS7oLfDt9wra8r7eQ sLbLIC0.3 t YAulmlZ wr5iighhotps4 UriePsmeZrwvFetdR.p s pMEaCdWe2 nwgintThC HINnVfki3nTictheB NGXeVoRmQeHtVrey2.d
G
6 + 14 x
Page7
-2-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Geometry
Name___________________________________
Secant Angles
Date________________ Period____
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
1)
2)
R
Q
R
S
?
50°
S
55°
? P
175°
F
140°
A
T
Q
3)
4)
T
U
175°
F
H
53° V ?
57°
175°
S
G
F
E
?
T
5)
6)
R
144°
B
Q ?
D
194°
?
P
C
7)
8)
70°
A
A
60°
E
T
S
V
120°
D
85°
C
?
U
B
?
Solve for x. Assume that lines which appear tangent are tangent.
9)
R
10)
12 x + 8
D
70°
Q
P
S
4x + 4
141 x − 1
©y Q2l0n1i1j XKUuct4az ESYo5fftLwEaFrUe7 NLuLtCj.Z x GAylylC RrYiSgWhUtDsq wrPeysAeQrSvneZdV.w g 6M9aCdeet QwRistchp YIqnPf8iNnIihtreU RGuecoPmje2tbr3yA.J
S
Q
R
50°
-1-
Page8
Worksheet by Kuta Software LLC
11)
12)
55°
H
15 x + 11
E
L
E
88°
60°
F
G
13)
S
C
D
5 x + 15
14)
9x − 3
P
E
F
C
9x − 7
124°
R
Q
G
17 x − 2
197°
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
16) Find m∠QPR
15) Find mKLM
R
K
8 x + 14
131°
M
5x − 1
S
26 x − 2
P
L
Q
18 x + 1
V
17) Find mRB
18) Find mBC
D
8 x + 11
5 x − 10
B
E
60°
C
8x + 6
C
A
R
F
B
9x − 7
D
13 x + 7
©4 n2o0n151b GK0uOt4aZ HSuoQfYtQwJaarWe2 DLxLvCS.n V WATlHlW orsiqgIh9t1ss Hrse9sJeurPvRekdI.z Y RM1aydWeh HwxietjhY xI2ntf2ixnDiDtieU 5GKekoBmmehtWreyx.t
Page9
-2-
Worksheet by Kuta Software LLC
Page10
Page11
Page12
6.3 Central/Inscribed Angles
Name_________________________
Find the value of x. Show work.
Find the value of x. Show work.
Page13