Angles and Arcs of 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 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 purple 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 Blank

Find the length of the arc in the diagram. ROUND your final answer to 2 decimal places.

Arc length = ______cm

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 Blank

Just type in the numeric value.

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 Blank

Solve for x. Just type in the numeric value.

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 Blank

Find the measure of minor arc SN (where the question mark is). Type in the numeric value.

Multiple Choice

Find the measure of  $$\angle KML$$ .

• $$m\angle KML=10\degree$$  

• $$m\angle KML=75\degree$$  

• $$m\angle KML=42.5\degree$$  

• $$m\angle KML=47.5\degree$$