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