Angles in Circles Remedial Worksheet



Central & Inscribed Angles Subtended by Arcs

Use this drawing to answer the questions below.

For questions 1 – 3, fill in the blank with “central” or “inscribed”.

1. [pic]FDG is a(n) _______________ angle.

2. [pic]AEB is a(n) _______________ angle.

3. [pic]AOB is a(n) _______________ angle.

For questions 4 – 6, indicate which angle each arc is subtended by.

4. [pic]AOB is subtended by arc _______.

5. [pic]FDG is subtended by arc _______.

6. [pic]ACB is subtended by arc _______.

For questions 7 – 9, fill in the missing angles.

7. The only central angle subtended by arc AB is __________

8. The two inscribed angles are subtended by the arc AB are __________ and __________

9. The angle subtended by arc FG is __________. It is a(n) ________________ (central / inscribed) angle.

Use this drawing to answer the questions below.

10. Minor arc PQ subtends the inscribed angle __________.

11. Darken major arc PQ on the diagram above. Major arc PQ subtends reflex [pic]POQ. This angle is indicated on the diagram. The inscribed angle subtended by major arc PQ is _________.

Using the Angle Properties

Use this drawing to answer the questions below.

1. The central angle subtended by arc JM is __________.

2. An inscribed angle subtended by the same arc is ____________.

3. Another inscribed angle subtended by the same arc is ___________.

4. Use angle properties 1 and 3 to explain the relationship between the measurements of the following angles:

a) [pic]JOM and [pic]JLM

b) [pic]JOM and [pic]JKM

c) [pic]JLM and [pic]JKM

Use this drawing to answer the questions below.

1. Which line segment in the diagram is a diameter? ______

2. According to angle property 2, the angle in the diagram that is a right angle is ___________. It is subtended by arc ______.

3. According to angle property 3, which angle in the diagram is equal to [pic]ADB?

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•

O

A

B

C

D

E

F

G

•

O

P

Q

R

S

(Recall: A reflex angle is an angle between 180° and 360°.)

•

J

K

L

M

O

A

O

•

B

D

C

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