Circles have different angle properties described by different circle theorems. Circle theorems are used in geometric proofs and to calculate angles.

Which circle theorem rule is used to find angle a?

Angles in the same segment are equal

The angle at the centre is twice the size of the angle at the circumference

Opposite angles of a cyclic quadrilateral add up to 180°

What is the size of angle a?

60°

120°

30°

Which circle theorem rule is used to find angle x?

A tangent meets a radius at 90°

The angle at the circumference in a semicircle is 90°

What is the size of angle x?

38°

142°

52°

Which circle theorem rule is used to find angle y?

Tangents which meet at the same point are equal in length

Alternate segment theory

The angle between a tangent and a radius is 90°

What is the size of angle y?

90°

Which circle theorem rule is used to find angle m?

Alternate segment theorem

Find the size of angle m.

70°

110°

20°

32°

64°

16°

72°

14°