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6.3 Arcs and Angles
Inscribed Angle Conjecture
The measure of an angle inscribed in a circle is ___________________ the measure of the central angle.
D
B
A
C
__________  ____________
Inscribed Angles Intercepting Arcs Conjecture
Inscribed angles that intercept the same arc are ________________.
D
B
A
E
C
_________  _________
Angles Inscribed in a Semicircle Conjecture
Angles inscribed in a semicircle are ____________________________.
B
A
C
O
D
E
________, ________, and ________ are right angles
Geometry Lesson 6.3: Arcs and Angles
Page 1
cyclic quadrilateral – A quadrilateral that is ________________ in a circle.
Cyclic Quadrilateral Conjecture
The opposite angles of a cyclic quadrilateral are ____________________.
B
C
A
D
______ and ______ are supplementary
______ and ______ are supplementary
Parallel Lines Intercepted Arcs Conjecture
Parallel lines intercept ________________ arcs on a circle.
B
C
D
A
________  ________
Geometry Lesson 6.3: Arcs and Angles
Page 2
Example 1: Find the missing measures.
74
a
128
98
b
c
a = _____
b = _____
d
c = _____
f
e
27
56
80
d = _____
e = _____
f = _____
Example 2: Find the missing measures.
a
50
c
b
35
e
d
45
f
a = _____
c = _____
e = _____
b = _____
d = _____
f = _____
Geometry Lesson 6.3: Arcs and Angles
Page 3
Example 3: Find the missing measures.
b
d
62
a
90
c
104
85
105
120
f
e
a = _____
c = _____
e = _____
b = _____
d = _____
f = _____
Example 4: Find the missing measures.
53
67
a
b
a = _____
b = _____
Example 5: Find the missing measures.
70
a 54
b
a = _____
Geometry Lesson 6.3: Arcs and Angles
c
57
b = _____
c = _____
Page 4
Example 6: Find the missing measures.
mRST= 240
mRST= 268
mRST= 306
R
R
R
S
S
T
T
T
S
mRST = _____
mRST = _____
mRST = _____
R
R
R
S
35
T
47
S
66
T
mRST = _____
Example 7: Find the value of y.
mPSQ = (3y – 15)
mPRQ = (2y + 15)
P
S
mRST = _____
mRST = _____
mPSQ = (2y – 10)
mPRQ = (y + 35)
mPSQ = (7y – 13)
mPRQ = (2y + 7)
P
Q
T
R
S
Geometry Lesson 6.3: Arcs and Angles
Q
R
S
y = _____
P
Q
R
S
y = _____
y = _____
Page 5
Example 8: Determine the measures of C, EBA, and DEB.
C
C
B
B
64
50
D
A
E
59
60
D
mC = _____
mC = _____
mEBA = _____
mEBA = _____
mDEB = _____
mDEB = _____
C
C
B
B
62
55
D
A
E
E
A
63
53
D
mC = _____
mC = _____
mEBA = _____
mEBA = _____
mDEB = _____
mDEB = _____
E
A
Homework: pp. 322 – 323 => 1 – 17; 22
Geometry Lesson 6.3: Arcs and Angles
Page 6
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