Lesson: Circles and Angles
An arc is part of a circle
An arc is part of a circle
A
C
B
An arc is part of a circle
so the curved line between AB would be abbreviated
A
C
B
An arc is part of a circle
so the curved line between AB would be abbreviated
AB
A
C
B
An arc is part of a circle
so the curved line between AB would be abbreviated
AB
A
with a curve over it.
C
B
An arc is part of a circle
so the curved line between AB would be abbreviated
AB
͡
A
with a curve over it.
C
B
Each arc has two descriptions
Each arc has two descriptions
A
C
B
Each arc has two descriptions
An arc measurement
A
C
B
Each arc has two descriptions
An arc measurement
A
80o
C
B
Each arc has two descriptions
An arc measurement
A
80o
100o
C
B
Each arc has two descriptions
An arc measurement, and an arc length
A
80o
100o
C
B
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
arc length is
in any unit
of distance
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
arc length is
in any unit
of distance
Arc measurement is in degrees
Each arc has two descriptions
radius = 1 in
An arc measurement, and an arc length
A
1.4 in
80o
100o
C
B
1.7 in
arc length is
in any unit
of distance
Arc measurements for the whole circle must equal 360o
A
80o
100o
C
B
Arc measurements for the whole circle must equal 360o
360 - 80 - 100
A
x
80o
100o
C
B
Arc measurements for the whole circle must equal 360o
360 - 80 - 100 = 180
A
x
80o
100o
C
B
Arc measurements for the whole circle must equal 360o
360 - 80 - 100 = 180
A
x
80o
100o
C
B
arc measurement
arc length
unit of distance
?
degrees
?
Which of the following is a unit of distance?
 degree
second
meter
feet
hours
grams
pounds
inches
If an angle has its vertex on the center of the circle
If an angle has its vertex on the center of the circle
If an angle has its vertex on the center of the circle
vertex on center
If an angle has its vertex on the center of the circle
then the angle measurement
If an angle has its vertex on the center of the circle
then the angle measurement
45o
If an angle has its vertex on the center of the circle
then the angle measurement
is equal to the arc measure
45o
If an angle has its vertex on the center of the circle
then the angle measurement
is equal to the arc measure
45o
45o
a
c
Which angle has its vertex on the center?
b
d
a
b
c
d
Find the angle measurements:
100o
60o
170o
Find the arc measurements:
100o
60o
170o
If the vertex of the angle is ON the circle
If the vertex of the angle is ON the circle
If the vertex of the angle is ON the circle
vertex on the
circle
If the vertex of the angle is ON the circle
then the arc measure
If the vertex of the angle is ON the circle
then the arc measure
40o
If the vertex of the angle is ON the circle
then the arc measure is divided by 2 to get the
40o
angle measure
If the vertex of the angle is ON the circle
then the arc measure is divided by 2 to get the
40o
20o
angle measure
Find the angle measures:
40o
200o
90o
Find the arc measures:
20o
100o
45o
An angle with the vertex ON the circle can also
look like this
An angle with the vertex ON the circle can also
look like this
An angle with the vertex ON the circle can also
look like this
vertex
on the
circle
Find the angle measures
120o
200o
Vertex ON center
Vertex ON circle
angle = arc/2
?
angle = arc
?
The vertex of an angle can be INSIDE the circle
The vertex of an angle can be INSIDE the circle
The vertex of an angle can be INSIDE the circle
vertex INSIDE
the circle
The vertex of an angle can be INSIDE the circle
but NOT on the center
The vertex of an angle can be INSIDE the circle
but NOT on the center
Center
The vertex of an angle can be INSIDE the circle
but NOT on the center
Center
not center
To find the angle,
To find the angle,
To find the angle,
add the arc of the angle
To find the angle,
add the arc of the angle
160o
To find the angle,
add the arc of the angle
and the arc opposite that arc
160o
To find the angle,
add the arc of the angle
and the arc opposite that arc
160o
40o
To find the angle,
add the arc of the angle
and the arc opposite that arc
add those arcs and divide by 2
160o
40o
To find the angle,
add the arc of the angle
and the arc opposite that arc
add those arcs and divide by 2
160o
40o
160 + 40 =
200
To find the angle,
add the arc of the angle
and the arc opposite that arc
add those arcs and divide by 2
160o
40o
160 + 40 =
200÷2=
To find the angle,
add the arc of the angle
and the arc opposite that arc
add those arcs and divide by 2
160o
40o
160 + 40 =
200÷2=
100
Find the angle measures
6o
10o
100o
10o
IN the circle
?
Where is the vertex for each angle?
ON the center
?
ON the circle
?
If the vertex of the angle is OUTSIDE the circle
If the vertex of the angle is OUTSIDE the circle
If the vertex of the angle is OUTSIDE the circle
vertex OUTSIDE
circle
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
105o
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
105o
35o
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
105o
35o
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
105o
35o
105 - 35
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
105o
35o
105 - 35 =
70
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
105o
35o
105 - 35 =
70 ÷ 2
If the vertex of the angle is OUTSIDE the circle
subtract the two arcs inside the angle
then divide by 2
105o
35o
105 - 35 =
70 ÷ 2 =
35o
Find the angle measures
200o
60o
180o
70o
260o
260o
100o
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