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Class 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.

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  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 pentagon add up to, in degrees? Give just the number.

  3. 3.One angle of a parallelogram is 65 degrees. What is the angle next to it, in degrees? Give just the number.

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

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

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

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

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

  6. 6.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

  7. 7.What do the four angles of any quadrilateral add up to, in degrees? Give just the number.

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

    • Hexagon
    • Octagon
    • Pentagon
    • Quadrilateral
    • Triangle

Answer key — Class 8 Maths — Understanding quadrilaterals

  1. 1. 115
  2. 2. 540
  3. 3. 115
  4. 4. 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
  5. 5. d) A square
  6. 6. d) All four sides are the same length
  7. 7. 360
  8. 8. 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Octagon