Angles in Circles Remedial Worksheet



Finding Missing Angles using Angles in a Circle Theorem

Use the diagrams to complete the sentence(s) following each one.

1. [pic]ACB is an inscribed angle subtended by arc ______. The central angle subtended by the same arc is __________. Therefore, the measurement of [pic]AOB is ______°.

2. [pic]ROT is a central angle subtended by arc ______. An inscribed angle subtended by the same arc is __________. Therefore, the measure of [pic]RST is ______°.

3. Reflex [pic]FOH is the central angle subtended by major arc ______. An inscribed angle subtended by the same arc is __________. Therefore, the measure of [pic]FGH is _____°.

4. [pic]RPQ is the inscribed angle subtended by major arc ______. Reflex [pic]_______ is also subtended by this same arc, and its measure is _______°. Therefore, the measure of [pic]RPQ is ______°.

5. Since the sum of angles in a quadrilateral is ______°, the measure of [pic]PRO is ______°.

Finding Missing Angles using Angles Inscribed in a Semicircle

Use the diagrams to complete the sentence(s) following each one.

1. The angle inscribed in a semicircle in the above diagram is _________. Therefore the measure of this angle is _____°.

2. Since it is inscribed in a semicircle, the measure of [pic]PQR is ______°.

3. Since the sum of angles in a triangle is ______°, the measure of [pic]PRQ is ______°.

4. The angle inscribed in a semicircle is _________. Its measure is _____°.

5. [pic]ABC is an isosceles triangle. This means that [pic]______ and [pic]______ are equal. Because the sum of angles in a triangle is 180°, this means that both of these angles measure _____°.

Finding Missing Angles using Inscribed Angles Subtended by the Same Arc

Use the diagrams to complete the sentence(s) following each one.

1. [pic]DAC is subtended by arc _____. Another inscribed angle subtended by the same arc is ________. Therefore the measure of [pic]DBC is ______°.

2. [pic]RSU is subtended by arc ______. Another inscribed angle subtended by the same arc is ________. Therefore the measure of [pic]RTU is ______°.

3. Another inscribed angle subtended by the same arc as [pic]SUT is __________. Therefore the measure of this angle is ______°.

4. By the inscribed angle property, the measure of [pic]WXZ is ______°, and the measure of [pic]XZY is ______°.

5. Since the sum of angles in a triangle is 180°, the measure of [pic]WVX is _______°.

Putting it All Together

In each of the following circles, use the angle properties to find the missing angles.

1. 2.

3. 4.

In each of the following circles, use the angle properties to find the missing angles. Justify your statements with reasons.

5. 6.

7. 8.

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•

A

B

C

O

37°

•

O

R

S

T

86°

•

O

F

H

G

216°

•

O

P

Q

R

70°

55°

•

O

J

K

L

•

O

P

Q

R

39°

•

O

A

B

C

A

43°

B

D

C

R

U

74°

21°

T

S

W

25°

X

V

18°

Z

Y

[pic]

[pic]

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