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Achievement objective GM6-4

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • deduce and apply the angle properties related to circles.


  • Finds unknown angles in circles using angle properties, including:
    • angle at centre is twice the angle at circumference on the same arc
    • angles subtended by the same arc are equal
    • radius perpendicular to the tangent
    • angle in a semi-circle equals 90°
    • opposite angles of a cyclic quadrilateral add to 180°
    • each exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.
  • Communicates reasoning, citing the angle properties used to solve problems.
  • See key mathematical ideas on NZmaths.


GM6-4 links to M7-5, M8-4.

Possible context elaborations

  • Proofs of the angle properties of circles.
  • Find unknown lengths and angles in circles and justify these using angle properties.

Assessment for qualifications

NCEA achievement standards at level 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The following achievement standard(s) could assess learning outcomes from this AO:

Last updated September 17, 2018