Geometrical Constructions

13 Grade 8 Mathematics questions on Geometrical Constructions, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   1 mark

   Find the size of each interior angle of a regular pentagon.

   A. 120 degrees

   B. 108 degrees

   C. 540 degrees

   D. 90 degrees

   (1 mark)

   Marking scheme

   B. $108$ degrees — the interior angles total $(5-2)\times 180=540$, shared between five: $540÷5=108$. C is the total rather than each angle, and A is a hexagon's interior angle.

2. Question 2

   1 mark

   Find the size of each interior angle of an equilateral triangle.

   A. 90 degrees

   B. 60 degrees

   C. 45 degrees

   D. 120 degrees

   (1 mark)

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3. Question 3

   1 mark

   Find the sum of the interior angles of a pentagon.

   A. 360 degrees

   B. 540 degrees

   C. 720 degrees

   D. 900 degrees

   (1 mark)

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4. Question 4

   3 marks

   Consider a regular octagon.

   (a) Find the sum of its interior angles. (2 marks)

   (b) Find the size of each interior angle. (1 mark)

   Marking scheme

   (a) The interior angles of a polygon with $n$ sides add up to $(n-2)\times 180^{\circ }$. (1)

   An octagon has $8$ sides, so the sum is $(8-2)\times 180^{\circ }=6\times 180^{\circ }=1080^{\circ }$. (1)

   (b) A regular octagon has all $8$ angles equal, so divide: $\frac{1080^{\circ }}{8}=135^{\circ }$. (1)

   Final answer: the angles sum to $1080^{\circ }$ and each one is $135^{\circ }$.

5. Question 5

   1 mark

   Find the sum of the interior angles of a hexagon.

   A. 540 degrees

   B. 900 degrees

   C. 1080 degrees

   D. 720 degrees

   (1 mark)

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6. Question 6

   3 marks

   Each interior angle of a regular polygon is 150 degrees. Find the number of sides.

   (3 marks)

   Marking scheme

   At each corner the interior and exterior angles lie on a straight line, so they add to $180^{\circ }$. (1)

   The exterior angle is therefore $180^{\circ }-150^{\circ }=30^{\circ }$. (1)

   The exterior angles of any polygon add up to $360^{\circ }$, so the number of sides is $\frac{360^{\circ }}{30^{\circ }}=12$. (1)

   Final answer: $12$ sides.

7. Question 7

   1 mark

   What is the sum of the exterior angles of any polygon?

   A. 180 degrees

   B. 540 degrees

   C. 360 degrees

   D. 720 degrees

   (1 mark)

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8. Question 8

   3 marks

   Four of the interior angles of a pentagon are 100, 110, 120 and 95 degrees. Find the fifth angle.

   (3 marks)

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9. Question 9

   1 mark

   Find the size of each interior angle of a regular hexagon.

   A. 120 degrees

   B. 720 degrees

   C. 108 degrees

   D. 135 degrees

   (1 mark)

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10. Question 10

    1 mark

    Find the sum of the interior angles of a quadrilateral.

    A. 180 degrees

    B. 270 degrees

    C. 360 degrees

    D. 540 degrees

    (1 mark)

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11. Question 11

    1 mark

    Find the size of each exterior angle of a regular octagon.

    A. 135 degrees

    B. 40 degrees

    C. 60 degrees

    D. 45 degrees

    (1 mark)

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12. Question 12

    1 mark

    A regular polygon has each exterior angle equal to 30 degrees. How many sides does it have?

    A. 12

    B. 6

    C. 10

    D. 15

    (1 mark)

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13. Question 13

    1 mark

    A regular polygon has 9 sides. Find the size of each exterior angle.

    A. 40 degrees

    B. 140 degrees

    C. 45 degrees

    D. 20 degrees

    (1 mark)

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