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Bellwork One-half of the measure of an angle plus its supplement is
equal to the measure of the angle. Find the measure of the angle
Solve for x 2x2-13x-7=0
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Bellwork Solution One-half of the measure of an angle plus its supplement is
equal to the measure of the angle. Find the measure of the angle
Solve for x 2x2-13x-7=0
APPLY OTHER ANGLES RELATIONSHIPS IN CIRCLES
Section 10.5
The Concept For the bulk of this chapter we’ve been dealing with the arc of
circles Today we’re going to finish out our discussion of arcs and
angles
TheoremTheorem 10.11
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc
A
C
BD
This makes sense if we think about this in terms of
an inscribed angle with only
one leg
On your own What is the measure of arc ADC
82oA
C
B
D
.41
.82
.164
A
B
C
On your own What is the measure of arc ABC
82oA
C
B
D
.16
.164
.196
A
B
C
On your own What is the measure of angle ACB, if arc CD measures 160o
35o
A
C
B
D
.35
.65
.130
A
B
C
TheoremsTheorem 10.12
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle
A
B
C
D
12m x mAB mCD
x
ExampleFind the measure of angle AEC
A
B
C
D
12m AEC mAC mBD
E
110o
96o
12 110 96
12 206
103
On your own What is the measure of angle ABC
225o
A
C
B
D
.30
.240
.480
A
B
C
E
255o
On your own What is the measure of angle ABD
148o
A
C
B
D
.89
.91
.178
A
B
C
E
30o
On your own What is the measure of arc AC
121o
A
C
B
D
.38
.81.5
.163
A
B
C
E
142o
TheoremsTheorem 10.13 Angles Outside the Circle Theorem
If a tangent and a secant, two tangents or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs
A
B
C
D
12m x mCD mAB
TheoremsFind the measure of angle ADB
A
B
D
12m ADB mACB mAB
250o
110o
C 1
2 250 110
12 140
70
On your own What is the measure of angle ABD
30o
A
C
B
D
.28
.56
.58
A
B
C
E
86o
On your own What is the measure of angle ADB
65o
A
B
D .65
.130
.260
A
B
C
195o
On your own What is the measure of arc BD
32o
A
B
D
.98
.100
.132
A
B
C
164o
On your own What is the measure of arc AB
22o
A
B
D
.49
.98
.142
A
B
C
120o
On your own What is the measure of angle of E, if arc ABC is 200o
A
B
D
.20
.40
.100
A
B
C
C
E
On your own What is the measure of angle of F?A
B
D
.15
.30
.95
A
B
C
C
F
110o
80o
On your own What is the measure of angle of F?A
B
D
.35
.32.5
.45
.50
A
B
C
D
C
F
35o
110o
105o
Homework
10.51-20, 22-25
Most Important Points Angle-Chord Relationships that
intercept inside a circle Angle relationship that intersects
outside the circle