11-4 Angle Measures and Segment Lengths

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11-4Angle Measures and Segment Lengths

• Theorems
• 11-11, 11-12
• Vocabulary
• Secant

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Theorem 11-11 (Angle Measures)

1. The measure of an angle formed by two lines that
   intersect inside a circle is half the sum of the
   measures of the intercepted arcs.

xo
1
yo
Secant
Secant
3
Theorem 11-11 (Angle Measures)

1. The measure of an angle formed by two lines that
   intersect outside a circle is half the difference
   of the measures of the intercepted arcs.

1
yo
xo
4
1 Finding Angle Measures

• Find the value of each variable.

46o
x
90o
5
2 Finding Angle Measures

• Find the value of each variable.

w
110o
70o
6
3 Finding Angle Measures

• Find the value of each variable.

110o
30o
y
7
Theorem 11-12 (Segment Lengths)
a
d

c
b
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Theorem 11-12 (Segment Lengths)
x
w

y
z
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Theorem 11-12 (Segment Lengths)
t

y
z
10
4 Finding Segment Lengths

• Find the value of the variable to the nearest
  tenth.

20
14
16
x
11
5 Finding Segment Lengths

• Find the value of the variable to the nearest
  tenth.

3
6.5
x
7