Free Printable Angle Properties and Circle Theorems

Worksheets

Angle Properties and Circle Theorems

Total questions: 71

Worksheet time: 4hrs 30mins

Name

Class

Date

What is the value of x and y?

x=75°; y=93°

x=65°;y=104°

x=75°; y=94°

x=65°; y=93

What is the size of angle x?

19^o

76^o

39^o

38^o

find the measure of angle a

120

what are the values of c and d?

c = 218, d = 71

d = 109, c = 71

c = 142, d = 218

c = 142, d = 109

What is the measure of angle c and d?

c = 21, d = 50

c = 63, d = 78

c = 78, d = 63

c = 10, d = 50

What are the sizes of a and b?

a = 57, b = 114

a = 57, b = 57

a = 114, b = 57

a = 57, b = 28.5

Find the value of the angle marked x....

100

Find the value of the angle marked x....

100

10.

Find the value of the angle marked x....

126

11.

Find the size of angle B. You do not need to include units.

(a)

12.

Find the size of angle ACB.

(a)

13.

Find the size of angle DAB

(a)

14.

Find the size of y.

(a)

15.

Find the angle POR.

(a)

16.

Find the angle ABC.

(a)

17.

find the measure of y

180

18.

Find the value of x.

19.

Two tangents CD and CB intersect circle A. Find the length of the tangent segment BC.

20.

In the diagram, the diameter of the circle is perpendicular to the chord. Solve for x.

21.

Line AB is a tangent to the circle. Find the value of each variable.

x = 34°

y = 11°

z = 15°

x = 65°

y = 69°

z = 46°

x = 46°

y = 69°

z = 65°

22.

What is m∠ACB?

67.5°

90°

22.5°

45°

23.

find the measure of angle a

120

24.

what are the values of c and d?

c = 218, d = 71

d = 109, c = 71

c = 142, d = 218

c = 142, d = 109

25.

What are the sizes of a and b?

a = 57, b = 114

a = 57, b = 57

a = 114, b = 57

a = 57, b = 28.5

26.

The angle between a radius and a tangent is _____________

180 degrees

90 degrees

Twice the angle at the centre

obtuse

27.

Find the value of the angle marked x....

28.

Find the value of the angle marked x....

100

29.

Find the value of the angle marked x....

30.

Find the value of the angle marked x....

102

129

31.

The angle at the centre (y) is _______ the angle (x) at the circumference.

twice

half

equal to

90 degrees

32.

The angle in a semi-circle is (a)

33.

The tangents to a circle from the same point will be

equal length

parallel

perpendicular

different lengths

34.

The angles in the same segment from a common chord are:

equal

30 degrees

add up to 90 degrees

35.

The opposite angles in a cyclic quadrilateral

are equal

add up to 180 degrees

add up to 360 degrees

are 90 degrees

36.

DAE is a tangent to a circle.

Write down the size of angle ABC. Give the reason for your answer

61 , alternate segments

61 , same segments

63, alternate segments

37.

The points E, F and G lie on the circumference of a circle, centre O.

JGH is a tangent to the circle.

Find the value of x and the value of y.

x=32 , y= 58

x=29, y=58

x=32 , y=32

38.

DAE is a tangent to a circle.

Write down the size of angle ABC. Give the reason for your answer

61 , alternate segments

61 , same segments

63, alternate segments

39.

What is the measure of angle A?

95°

169°

191°

79°

40.

Select the Corresponding angle(s)

41.

How many degrees are there in a triangle?

180

360

Every triangle is different

42.

Solve for x.

$62\degree$

$118\degree$

$28\degree$

$45\degree$

43.

Angles a and b sum to 180 degrees.

These are examples of...

Supplementary angles

Co-interior angles

Vertically Opposite angles

Alternate angles

44.

Calculate the value of angle x.

$112\degree$

$90\degree$

$22\degree$

$68\degree$

45.

Which are pairs of vertical angles?

∠COB & ∠COA

∠AOD & ∠AOC

∠COB & ∠AOD

∠BOD & ∠AOD

46.

What are vertical angles?

Angles that are adjacent to each other

Angles that add up to 180°

Angles that are opposite of each other when lines intersect

47.

What is the value of angle a?

150

140

130

48.

5) True or False.

If the following parallel lines are cut by a transversal, would

\angle2

and

\angle6

be corresponding?

True. They are in matching corners.

False. They are co-interior

49.

What is the relationship of the Angles

Alternate Interior

Alternate Exterior

Corresponding

Same Side Interior

50.

What is the measure of x?

x = 118

x = 108

x = 28

x = 58

x = 62

51.

What relationship exists between angles 1 and 2

Corresponding angles

Supplementary angles

Vertical angles

Alternate Exterior Angles

52.

The diagram shows a circle, centre O.

What is the value of x

106

53.

The diagram shows a circle, centre O.

What is the value of z.

116

244

122

54.

The diagram shows a circle, centre O.
Points A, B, C and D lie on the circumference.
AB=BC
What is the value of angle ADC

104

55.

The diagram shows a circle, centre O.
P, Q, R and S are points on the circumference.
Select all the correct statements.

Angle QPS = Angle QRS = 90, because right angle in a semicircle

Angle SQP=27, because tangent is perpendicular to the radius

Angle PSQ=63, because angle in alternate segment

Angle SPQ=27, because angles in the same segment

56.

The diagram shows a circle, centre O.

What is the value of w.

104

57.

The diagram shows circle with AB as a diameter.

Angle BAC and ACB are in the ration 5:7.

What is the value of BAC.

37.5

52.5

58.

A, B, C, D, and E lie on a circle, centre O.

What are the values of p and q?

p=30, q=18

p=18, q=30

p=36, q=15

p=20, q=30

59.

AD is a diameter of the circle ABCDE.

AB and ED are parallel lines.

What are the values of w, x, y and z?

w=30, x=22, y=30, z=52

w=30, x=30, y=22, z=52

w=52, x=22, y=30, z=30

w=22, x=30, y=22, z=52

60.

The diagram shows a circle, centre O.

What is the value of x

106

61.

The diagram shows a circle, centre O.

What is the value of z.

116

244

122

62.

The diagram shows a circle, centre O.
Points A, B, C and D lie on the circumference.
AB=BC
What is the value of angle ADC

104

63.

The diagram shows a circle, centre O.
P, Q, R and S are points on the circumference.
Select all the correct statements.

Angle QPS = Angle QRS = 90, because right angle in a semicircle

Angle SQP=27, because tangent is perpendicular to the radius

Angle PSQ=63, because angle in alternate segment

Angle SPQ=27, because angles in the same segment

64.

The diagram shows a circle, centre O.

What is the value of w.

104

65.

The diagram shows circle with AB as a diameter.

Angle BAC and ACB are in the ration 5:7.

What is the value of BAC.

37.5

52.5

66.

A, B, C, D, and E lie on a circle, centre O.

What are the values of p and q?

p=30, q=18

p=18, q=30

p=36, q=15

p=20, q=30

67.

AD is a diameter of the circle ABCDE.

AB and ED are parallel lines.

What are the values of w, x, y and z?

w=30, x=22, y=30, z=52

w=30, x=30, y=22, z=52

w=52, x=22, y=30, z=30

w=22, x=30, y=22, z=52

68.

P, Q, R and S lie on a circle centre O.

TP and TQ are tangents to the circle.

What are the values of w, x and y?

w=26, x=128, y=52

w=32, x=64, y= 26

w=26, x=116, y=54

w=26, x=128, y=62

69.

A,B, C, and D lie on a circle, centre O.

SCT is a tangent and is parallel to OB.

What are the values of x, y, z and the reflex angle AOC.

x=40, y=20, z=120, reflex angle AOC=130

x=40, y=25, z=115, reflex angle AOC=230

x=40, y=25, z=115, reflex angle AOC=130

x=40, y=25, z=130, reflex angle AOC=230

70.

A,B, C, and D lie on a circle, centre O.

SCT is a tangent and is parallel to OB.

What are the values of x, y, z and the reflex angle AOC.

x=40, y=20, z=120, reflex angle AOC=130

x=40, y=25, z=115, reflex angle AOC=230

x=40, y=25, z=115, reflex angle AOC=130

x=40, y=25, z=130, reflex angle AOC=230

71.

P, Q, R and S lie on a circle centre O.

TP and TQ are tangents to the circle.

What are the values of w, x and y?

w=26, x=128, y=52

w=32, x=64, y= 26

w=26, x=116, y=54

w=26, x=128, y=62

100 %

Angle Properties and Circle Theorems

Total questions: 71

Worksheet time: 4hrs 30mins

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