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Year 8 Maths — Understanding quadrilaterals

Work out the angles in a polygon and use the properties of parallelograms, rhombuses, rectangles and squares.

Name: ________________________

Before you start

The four corners of this parallelogram hold four angles. Find out how big each one is — nothing here is right or wrong.

1234
  1. 1. Angle A — 45°
  2. 2. Angle B — 135°
  3. 3. Angle C — 45°
  4. 4. Angle D — 135°

Opposite corners match. Any two corners next to each other add up to 180°, which is why one known angle gives you all four.

  1. 1.Three angles of a quadrilateral are 80, 100 and 65 degrees. What is the fourth, in degrees? Give just the number.

  2. 2.What do the interior angles of a hexagon add up to, in degrees? Give just the number.

  3. 3.Which of these is true of every rhombus but not of every rectangle?

    • a) Opposite sides are parallel
    • b) Opposite angles are equal
    • c) The angles add up to 360 degrees
    • d) All four sides are the same length

  4. 4.What do the interior angles of a pentagon add up to, in degrees? Give just the number.

  5. 5.Sort each property by whether it is true of every parallelogram.

    Groups: True of every parallelogram · Not true of every parallelogram

    • Every angle is a right angle
    • The diagonals cut each other in half
    • All four sides are equal
    • Opposite angles are equal
    • The diagonals are equal in length
    • Opposite sides are equal

  6. 6.Each exterior angle of a regular polygon is 45 degrees. How many sides has it?

  7. 7.In which quadrilateral do the diagonals always cross at right angles and always come out the same length?

    • a) A parallelogram
    • b) A square
    • c) A rectangle
    • d) A rhombus

  8. 8.Put these polygons in order by what their interior angles add up to, smallest first.

    • Octagon
    • Hexagon
    • Quadrilateral
    • Pentagon
    • Triangle

Answer key — Year 8 Maths — Understanding quadrilaterals

  1. 1. 115
  2. 2. 720
  3. 3. d) All four sides are the same length
  4. 4. 540
  5. 5. Opposite sides are equal → True of every parallelogram; Opposite angles are equal → True of every parallelogram; The diagonals cut each other in half → True of every parallelogram; All four sides are equal → Not true of every parallelogram; The diagonals are equal in length → Not true of every parallelogram; Every angle is a right angle → Not true of every parallelogram
  6. 6. 8
  7. 7. b) A square
  8. 8. 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Octagon