Central Angles

P

A

BC

Central Angle : An Angle whose vertex is at the center of the

circleMinor ArcMajor Arc

Less than 180°

More than 180°

ABACB

To name: use 2 letters

To name: use 3 letters

<APB is a Central Angle

P

E

F

D

Semicircle: An Arc that equals 180°

EDF

To name: use 3 letters

EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of

180°

THINGS TO KNOW AND REMEMBER ALWAYS

A circle has 360 degrees

A semicircle has 180 degrees

Vertical Angles are Equal

Linear Pairs are Supplementary

Vertical Angles are Equal

Linear Pairs are Supplementary

http://www.mathopenref.com/linearpair.html

120° 60°

measure of an arc = measure of central angle

A

B

C

Q 96

m AB

m ACB

m AE

E

=

=

=

96°

264°

84°

Arc Addition PostulateA

B

C

m ABC =

m AB + m BC

Tell me the measure of the following arcs.

80100

40

140A

B

C

D

R

m DAB =

m BCA =

240

260

Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles.

4545

A

BC

D

110

Classwork

•Page 193 #9-18 You have 15 minutes.

Inscribed Angle: An angle whose

vertex is on the circle and

whose sides are chords of the circle

INSCRIBEDANGLE

INTER

CEP

TED

ARC

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

C

L

O

T1.

YES; CL

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.

Q

R

K

V2. NO;

QVR

S

2

ArcdIntercepteAngleInscribed

160°

80°

To find the measure of an inscribed angle…

http://www.geogebra.org/

en/upload/files/english/Guy/

Circles_and_angles/Inscribed_Anlge.html

120

x

What do we call this type of angle?What is the value of x?

y

What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the

measure of the inscribed arc!!

http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html

Examples

3. If m JK = 80, find m <JMK.

M

Q

K

S

J

4. If m <MKS = 56, find m MS.

40

112

72

If two inscribed angles intercept the same arc, then they are congruent.

http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_angle_practice.html

Example 5

In J, m<A= 5x and m<B = 2x + 9.Find the value of x.

A

Q

D

JT

U

B

m<A = m<B 5x = 2x+9x = 3

Classwork:

•Page 193 #9-23•Page 207 #1-15

Whatever is left is homework