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Grade 5 Math — 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.Match each regular polygon to the size of one of its exterior angles, in degrees.

    • Equilateral triangle
    • Square
    • Regular pentagon
    • Regular hexagon
    • Regular decagon
    • 90
    • 60
    • 120
    • 36
    • 72

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

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

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

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

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

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

  6. 6.The diagonals of a parallelogram cross at the middle. One diagonal is cut into two pieces of 5 inches each. How long is that whole diagonal, in inches? Give just the number.

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

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

Answer key — Grade 5 Math — Understanding quadrilaterals

  1. 1. Equilateral triangle → 120; Square → 90; Regular pentagon → 72; Regular hexagon → 60; Regular decagon → 36
  2. 2. 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
  3. 3. 540
  4. 4. 115
  5. 5. 360
  6. 6. 10
  7. 7. 720
  8. 8. 115