Angle and Arcs in a Circle

Angle and Arcs in a Circle

Central Angles and Arc

MGSE9-12.G.C.1 Understand that all circles are similar.

MGSE9-12.G.C.2 Identify and describe relationships among

inscribed angles, radii, chords, tangents, and secants. Include

the relationship between central, inscribed, and circumscribed

angles; inscribed angles on a diameter are right angles; the

radius of a circle is perpendicular to the tangent where the

radius intersects the circle.

Intro to Arc in a cirlce

Hey guys remember a circle 360 degrees and a portion of a circle is called an Arc, which looks like a slice of pizza. There are three types of Arcs called Minor, Major, and Semicircle.

Multiple Choice

How many degrees does a circle have?

• less than 180

• equal to 180

• more than 180

• 360

Arc Labels

• A minor arc is labeled with 2 letters, for example AX

Multiple Choice

How many degrees does a major arc have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Choice

How many degrees does a semicircle have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Choice

How many degrees does a minor arc have?

• less than 180

• equal to 180

• more than 180

• 360

Multiple Select

Check all that is true about the Arcs in the circle

• XB is a Major Arc

• XAY is a semicircle

• XYA is a Major Arc

• XB is a semicircle

Things to know as we find the measure of an Arc.

• There are 360 degrees in a circle

• There are 180 degrees in a semicircle

• A diameter a line that goes though the center of a circle splitting the into two semicircles.

• Central angle is where two radii form an angle at the center of a circle.

• The measure of the arc equal to the measure of the central angle

Identify Arc angles

• Central angle is where two radii meet at the center of the circle.

• Arc angle equal to the central angle

• Inscribed Angle: an angle made from points sitting on the circle's circumference.

• Central angles are subtended by an arc between those two points

• The vertex is the center of the circle.

Multiple Choice

A ____ angle is an angle whose vertex is a the center of a circle.

• supplementary
• complimentary
• central
• obtuse

Multiple Choice

What is the value of x?

• x = 160

• x = 40

• x = 80

• x = 360

Multiple Choice

What is the measure of arc AB?

• 140
• 142
• 180
• 153

Angles in Circles

How to find arcs/angles in a circle

Central angle: angle=arc

Central angles have a vertex at the center of the circle. The arc created by the two radii is equal to the angle.

Fill in the Blank

What is x?

Inscribed Angle: angle=1/2*arc or arc=2*angle

Inscribed angles must have a vertex touching the circle. The angle is half of the outside arc or the arc is twice the angle inside.

Fill in the Blank

What is x?

Two Tangents: angle+arc=180

Two tangents create an angle and an arc (small arc). These two added together always equal 180.

Fill in the Blank

What is x equal to?

External: angle=1/2(big arc - little arc)

When two secants meet outside of a circle, the angle is equal to half of the different of the arcs.

Fill in the Blank

What is the measure of the missing angle?

Internal: angle=1/2(big arc + little arc)

When two secants meet inside the circle, the angle is equal to half of the sum of the arcs.

Fill in the Blank

What is the measure of the internal angle?

Inscribed Quadrilateral: opposite angles =180

When a quadrilateral is inscribed in a circle, the opposite angles always add to 180.

Multiple Select

Select all equations that can be used to solve for x and y in the following inscribed quadrilateral.

• x+55=180

• y+85=180

• x+85=180

• y+55=180

Multiple Choice

The term when you have more than one radius.

• radii

• circle

• chord

• semicircle

Multiple Choice

The set of all points in a plane that are given distance from a given point.

• circumference

• Circle

• semi circle

• tangent line

Multiple Choice

The line segment that has endpoints on a circle and passes through the center of the circle.

• radius

• minor arc

• diameter

• secant line

Multiple Choice

The distance around the circle.

• congruent circles

• semicircle

• arc

• circumference

Multiple Choice

An arc of a circle whose endpoints are the endpoints of a diameter.

• semicircle

• major arc

• minor arc

• circle

Multiple Choice

A continuous part of a circle between two points on the circle.

• circle

• arc

• circumference

• tangent line

Multiple Choice

An angle whose vertex is the center and whose sides are the radii of the circle.

• radius

• arc

• central angle

• secant line

Multiple Choice

A line segment whose endpoints are on a circle.

• semicircle

• concentric circles

• chord

• sector of a circle

Multiple Choice

An angle whose vertex is on the circle and whose sides are chords of the circle.

• adjacent arcs

• diameter

• Inscribed angle

• arc

Multiple Choice

Is the intersection of the tangent line and a point on the side of the circle.

• arc

• Point of tangency

• secant line

• radii

Multiple Choice

The given point from which all points on a circle are equidistant.

• arc

• radius

• center or a circle

• chord

Multiple Choice

A line that intersects a circle in exactly two points.

• diameter

• central angle

• arc

• secant line

Multiple Choice

Circles who's radii are congruent.

• congruent circles

• circumference

• sector of a circle

• major arc

Multiple Choice

Circles that lie in the same plane and have the same center.

• arc

• concentric circles

• central angle

• secant line

Multiple Choice

An arc that is larger than the semicircle.

• semicircle

• circle

• major arc

• adjacent arcs.

Multiple Choice

A region of a circle bounded by an arc of the circle and two radii to the arc's endpoints.

• chord

• second line

• radii

• sector of a circle

Multiple Choice

Arcs on the same circle that have exactly one point in common.

• adjacent arcs

• circle

• point of tangency

• minor arc

Multiple Choice

An arc that is smaller than a semicircle.

• radii

• minor arc

• tangent line

• central angle

Multiple Choice

A line that intersects a circle in exactly one point.

• tangent line

• arc

• radius

• diameter

Multiple Choice

A line segment that has one endpoint on a circle and the other endpoint at the center of the circle.

• circle

• central angle

• radius

• arc

Multiple Choice

What is the measure of angle K and angle M?

• $$m\angle K=100\ \ \ \ \&\ \ \ m\angle M=100$$

• $$m\angle K=50\ \ \ \ \&\ \ \ m\angle M=50$$

• $$m\angle K=100\ \ \ \&\ \ \ m\angle M=50$$

• $$m\angle K=50\ \ \ \&\ \ \ m\angle M=100$$

Multiple Choice

Find x.

• 51

• 25.5

• 102

• 67

Multiple Choice

Find a and b.

• a=74 degrees
  b=93 degrees
• a=93 degrees
  b=74 degrees
• a=87 degrees
  b=106 degrees
• a=106 degrees
  b=87 degrees

Multiple Choice

What is the measure of arc EAB  in circle F?

• 72

• 92

• 148

• 200

Match

Match the following part of the circle with its correct label.

• Center

• Chord

• Radius

• Diameter

• Tangent Line

Point S

Segment XW

Segment ST

Segment QV

Line VU

• Point S

• Segment XW $$\overline{XW}$$

• $$\overline{ST}$$

  Segment ST

• $$\overline{QV}$$

  Segment QV

• $$\overline{VU}$$

  Line VU

Match

Match the following vocabulary term with its appropriate part of the circle.

• Secant Line

• Point of Tangency

• Minor Arc

• Major Arc

• Semi-Circle

Line PR

Point V

Arc QP

Arc RVT

Arc QXV

• Line PR

• Point V

• $$\cap QP$$

  Arc QP

• $$\cap RVT$$

  Arc RVT

• $$\cap QXV$$

  Arc QXV

Multiple Choice

What is the measure of angle 1?

• 130
• 65
• 44
• 86

Multiple Choice

What is the measure of angle 2?

• 115°

• 65°

• 21°

• 90°

Multiple Choice

What is the m∠A?

• 20
• 40
• 60
• 30

Multiple Choice

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

• 93°

• 137°

• 120°

• 102°

Math Response

Find the measure of the missing angle in degrees.

Type answer here

Correct Answer: 41

Deg^°

Rad

Multiple Choice

What is the measure of arc PR ?

• 360º

• 45º

• 90º

• 180º

Multiple Choice

Determine the measure of Arc PG.

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A

• B

• C

• D

Match

Match the answers to the following problems.

• $$3\pi$$

• $$\frac{21\pi}{2}$$

• $$5\pi$$

• $$\frac{289\pi}{12}$$

Problem 1

Problem 4

Problem 3

Problem 2

• Problem 1

• Problem 4

• Problem 3

• Problem 2

Multiple Choice

Calculate the area of the sector.

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

If the length of the 45° region of this circle is $$10\Pi$$   inches, what is the radius of the circle?

• 40 in.

• $$4\sqrt{5}$$  in.

• 10 in.

• 20 in.

Multiple Choice

Which angles are congruent?

• <ACB = <ADB
• <ADB=<AEB
• <AEB=<ACB
• <ACB = <ADB = <AEB

Fill in the Blank

In the circle, angle BAC = (30+4x)° and angle CDB = (90-2x)°. What is the measure of arc BC?

Multiple Choice

Determine the value of x using the information in the diagram.

• 60º

• 70º

• 80º

• 100º

Multiple Choice

Sarah is trying to determine how much more pie she would get from a slice of two different pieces. 1 slice has an angle of 64° and a diameter of 14 inches. The other slice has an angle of 64° and a diameter of 11 inches.

• 13

• 12.78

• 10.47

• 19.33