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Geometry: angles and shapes

Geometry questions test angle facts, perimeter, area and properties of 2D and 3D shapes. Harder and written (Stage 2) papers may combine angles with algebra.

What is tested

  • Angles in triangles, on a straight line and around a point
  • Perimeter and area of rectangles, triangles and compound shapes
  • Properties of shapes, symmetry, coordinates

Worked example

Two angles in a triangle are 65° and 48°. Find the third angle.

  1. Angles in a triangle add to 180°.
  2. 65° + 48° = 113°.
  3. 180° − 113° = 67°.

Answer: 67°

Exam-day checklist

  • Write the angle fact you are using (180° on a line, 360° around a point).
  • Label the diagram with what you know.
  • Give units: degrees, cm, cm².
  • For compound shapes, split into rectangles.

Common mistakes

  • Mixing up perimeter and area.
  • Using 360° for a triangle.
  • Forgetting the ½ in the area of a triangle.

Try it yourself

1. A rectangle is 12 cm by 5 cm. Find its perimeter and area.

Show answer

Perimeter 34 cm; area 60 cm²

Perimeter = 2 × (12 + 5) = 34. Area = 12 × 5 = 60.

2. Angles on a straight line are 118° and x. Find x.

Show answer

62°

Angles on a line add to 180°: 180 − 118 = 62.

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More topic guides

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