Angles and Arcs of Circles

Angles and Arcs in Circles

Angles and Arcs in Circles

Angles and Arcs in Circles

Objectives

• Identify central angles, minor arcs, major arcs, semicircles and find their measures

• Find arc lengths

Multiple Choice

Which of the following best represents line GH?

• tangent

• chord

• segment

• secant

Multiple Choice

Which of the following best represents line BK?

• tangent

• chord

• segment

• secant

Multiple Select

Which of the following best represents the point of tangency in circle J?

• A

• E

• K

• G

What is a Central Angle?

A central angle is an angle whose vertex is at the center of the circle and is formed by two radii.

Ways to label angles

Multiple Select

Choose the correct way(s) to label the angle.

• $$\angle ABC$$

• $$\angle CBA$$

• $$\angle B$$

• $$\angle C$$

Ways of Labeling Arcs

• Use the endpoints of the arc:

• CB or BC would be the blue arc

• CDB or BDC would be the red arc (use points in-between endpoints to indicate which direction to go in)

• Arc CBD (Start at C, go to B then go to D)

Multiple Select

Correctly choose the correct names for the central angle and its intercepted arc

• $$\angle CDA$$ ; Arc BD

• $$\angle FEB$$ ; Arc BCF

• $$\angle CAD$$ ; Arc CFD

• $$\angle CFE$$ ; Arc BED

Multiple Select

Choose the correct way to label the pink arc

• CB

• CAB

• AB

• BAC

• CDB

Labeling arcs and angles

Multiple Select

Check the boxes that have the correct label for the red arc.

• CDB

• CB

• D

• CAB

• BDC

Labeling Inscribed Angles and Arcs

Multiple Select

Correctly choose the correct names for the inscribed angle and its intercepted arc

• $$\angle CDA$$ ; Arc BD

• $$\angle FEB$$ ; Arc BFD

• $$\angle CAD$$ ; Arc CFD

• $$\angle CFE$$ ; Arc BED

Fill in the Blanks

Today we are going to learn about the following:

• Central Angle

• Inscribed Angle

• Interior Angle

• Exterior Angle

Central Angle

• A central angle of a circle has a vertex at the center and is formed by two radii.

• The measure of the central angle is the same as the measure of its corresponding arc of the circle.

Multiple Choice

Find the measure of  $$\angle AOB$$   

• $$m\angle AOB=27\degree$$  

• $$m\angle AOB=333\degree$$  

• $$m\angle AOB=207\degree$$  

• $$m\angle AOB=13.5\degree$$  

Inscribed Angle

• An inscribed angle in a circle has a vertex on the circle and is formed by two chords.

• The measure of an inscribed angle is half the measure of its corresponding arc of the circle.

Fill in the Blanks

Multiple Choice

• $$m\angle PQR=68\degree$$

• $$m\angle PQR=34\degree$$

• $$m\angle PQR=292\degree$$

• $$m\angle PQR=112\degree$$

Exterior Angle

Fill in the Blanks

Interior Angle

• An interior angle has a vertex inside the circle and is formed by two intersecting chords/secants.

• The measure of an interior angle is half the sum of its corresponding arcs.

• (arc1 + arc2)/2

Multiple Choice

What is the measure of the angle DBC?

• $$m\angle DBC=65\degree$$

• $$m\angle DBC=87.5\degree$$

• $$m\angle DBC=120\degree$$

• $$m\angle DBC=62.5\degree$$

Fill in the Blanks

Multiple Choice

Find the measure of  $$\angle KML$$ .

• $$m\angle KML=10\degree$$  

• $$m\angle KML=75\degree$$  

• $$m\angle KML=42.5\degree$$  

• $$m\angle KML=47.5\degree$$