Circle Theorems

These are the first three theorems that were introduced in class.​

Circle Theorems 1-3​

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Multiple Choice

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

• 90

• 43

• 47

• 53

Multiple Choice

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

• 50

• 100

• 80

• 90

Multiple Choice

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

• 125

• 70

• 110

• 55

Multiple Choice

If a is 60⁰ , what is 2a ?

• 30⁰
• 120⁰
• 90⁰

Multiple Choice

How many degrees is angle c ?

• 20

• 45

• 70

• none of the above

Multiple Choice

How many degrees is angle d ?

• 20

• 45

• 70

• none of the above

Multiple Choice

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

• 56

• 90

• 34

• 44

Multiple Choice

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

• 90

• 45

• 50

• 100

Multiple Choice

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

• 76

• 38

• 152

• 14

Multiple Choice

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

• 88

• 75

• 92

• 102

Multiple Choice

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

• 61

• 63

• 117

• 119

Multiple Choice

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

• 32

• 64

• 16

• 58

Multiple Choice

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

• 90

• 43

• 47

• 53

Multiple Choice

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

• 50

• 100

• 80

• 90

Multiple Choice

How many degrees is angle a?

• 30

• 27

• 60

• 63

Multiple Choice

How many degrees is angle b ?

• 30

• 27

• 60

• 63

Multiple Choice

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

• 102

• 51

• 129

• 78

Multiple Choice

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

• 63

• 126

• 54

• 90

All vertices of the cyclic quadrilateral must touch the circumference of the circle.​

Theorem 4 and 5 are outlined below the diagram.​

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​Cyclic Quadrilaterals

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Multiple Choice

Which circle does not have cyclic quadrilateral?

Multiple Choice

∠x + ∠y =

• 45°

• 900°

• 180°

• 360°

Multiple Choice

x =

• x = 8.5°

• x = 9.5°

• x = 76°

• x = 98°

Multiple Choice

y =

• y = 8°

• y = 20.5°

• y = 82°

• y = 98.5°

Multiple Choice

y is equal in measure to ______.

• n

• m

• x

• z

Multiple Choice

x =

• 22°

• 38°

• 79°

• 158°

Multiple Choice

y =

• 66°

• 75°

• 105°

• 114°

Multiple Choice

x =

• 66°

• 75°

• 105°

• 114°

Multiple Choice

x =

• 40°

• 50°

• 70°

• 120°

Multiple Choice

Find the sizes of the lettered angles in each of these circles

• a = 50, b = 95

• a = 85, b = 130

• a = 95, b = 50

• a = 130, b = 85

Multiple Choice

Find the sizes of the lettered angles in each of these circles

• p=68, q=44

• p = 136, q=65

• p=44, q=68

• p=88, q=136

Multiple Choice

Find the values of x and y in each of these circles where O is the centre.

• x = 133°​

  y = 47°

• x = 26°​

  y = 128°

• x = 55°​

  y = 125°

• x = 48°​

  y = 78°

Multiple Choice

Find the values of x and y in each of these circles where O is the centre.

• x = 50°​

  y = 45°

• x = 45°​

  y = 48°

• x = 48°​

  y = 40°

• x = 48°​

  y = 45°