Sec 2 G2 Maths Quadrilaterals and polygons worksheet with answers

A free Sec 2 G2 Maths worksheet on quadrilaterals and polygons: 9 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 2 G2 Maths worksheet: Quadrilaterals and polygons

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

The diagram shows a plus sign. Write down the number of lines of symmetry of the shape.

Answer[1]

The diagram shows a rectangle. Write down its order of rotational symmetry.

Answer[1]

The diagram shows a quadrilateral

ABCD

. Find

x

Answer[2]

(a)State whether the following statement is true or false. Every square has diagonals of equal length.

Answer (a)[1]

(b)State whether the following statement is true or false. Every rhombus has four equal sides.

Answer (b)[1]

The diagram shows a bow-tie shape. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

Answer°[2]

The diagram shows part of a regular polygon

ABCD\ldots

with the diagonal

AC

\angle BAC = 30^\circ

. Find the number of sides of the polygon.

Answer[3]

Section B

(a)The diagram shows the letter F. State whether the dashed line is a line of symmetry of the shape.

Answer (a)[1]

(b)The marks on the diagram show what is known about quadrilateral

ABCD

. Write down the most special name of

ABCD

Answer (b)[1]

(c)

ABCD

is a rhombus. Find

x

Answer (c)[2]

(d)The diagram shows a regular pentagon. Find

x

Answer (d)[2]

(a)The diagram shows the letter H. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

Answer (a)°[2]

(b)(i)Each interior angle of a regular polygon is

8

times each of its exterior angles. Find the number of sides of the polygon.

Answer (b)(i)[2]

(b)(ii)Can

144^\circ

be each interior angle of a regular polygon? Choose the answer with its reason.

Answer (b)(ii)[2]

(a)The diagram shows an arrow. State whether the dashed line is a line of symmetry of the shape.

Answer (a)[1]

(b)The diagram shows a bow-tie shape. Find the smallest angle through which it can be rotated about its centre to look exactly the same.

Answer (b)°[2]

(c)

ABCD

is a rectangle. Its diagonals meet at

O

, and

\angle OAB = 64^\circ

. Find

x

Answer (c)°[2]

(d)The diagram shows a quadrilateral

ABCD

. Find

x

Answer (d)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

\text{Number of lines of symmetry} = 4

[1]

Lines of symmetry: one along each arm and the two diagonals.

\text{Number of lines of symmetry} = 4

Question 2

Answer:

\text{Order} = 2

[1]

It looks the same every half turn.

\text{Order} = 2

Question 3

Answer:

x = 54

[2]

70^\circ + (2x - 10)^\circ + (2x + 30)^\circ + x^\circ = 360^\circ

(∠ sum of quad.)

5x + 90 = 360

5x = 270

x = 54

Question 4

(a)Answer: TRUE[1]

Every square has diagonals of equal length.True.

(b)Answer: TRUE[1]

Every rhombus has four equal sides.True.

Question 5

Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

Question 6

Answer:

n = 6

[3]

\angle ABC = 180^\circ - 2 \times 30^\circ

\phantom{\angle ABC} = 120^\circ

(∠ sum of △)Exterior angle

= 180^\circ - 120^\circ

= 60^\circ

n = \dfrac{360}{60}

n = 6

Question 7

(a)Answer: NO[1]

Each corner on one side must land exactly on a corner on the other side, and each side on a side.No: the two halves do not match when folded, so the dashed line is not a line of symmetry.

(b)Answer: isosceles trapezium[1]

Equal sides: one pair.Parallel sides: one pair.Right angles: none marked.One pair of parallel sides, the other two sides equal and equal base angles: an isosceles trapezium.

(c)Answer:

x = 28

(∠ sum of △)[2]

\angle BCA = x^\circ

(base ∠s of isos. △)

x^\circ + x^\circ + 124^\circ = 180^\circ

2x = 56

x = 28

(∠ sum of △)

(d)Answer:

x = 108

(∠ sum of polygon)[2]

(5 - 2) \times 180^\circ = 540^\circ

x = \dfrac{540}{5}

x = 108

(∠ sum of polygon)

Question 8

(a)Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

(b)(i)Answer:

n = 18

[2]

8 + 1 = 9

units

\rightarrow 180^\circ

1

unit

\rightarrow \dfrac{180}{9} = 20^\circ

Exterior angle

= 20^\circ

n = \dfrac{360}{20}

n = 18

(b)(ii)Answer: YES[2]

Exterior angle

= 180^\circ - 144^\circ

= 36^\circ

\dfrac{360}{36} = 10

It is a whole number: a regular 10-sided polygon has interior angles of

144^\circ

Question 9

(a)Answer: YES[1]

Each corner on one side must land exactly on a corner on the other side, and each side on a side.Yes: the two halves fold exactly onto each other, so the dashed line is a line of symmetry.

(b)Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

(c)Answer:

x = 26

°[2]

\angle OBA = 64^\circ

(base ∠s of isos. △)

x = 90 - 64

x = 26

(d)Answer:

x = 52

[2]

(2x - 10)^\circ + (2x + 30)^\circ + x^\circ + 80^\circ = 360^\circ

(∠ sum of quad.)

5x + 100 = 360

5x = 260

x = 52

Sec 2 G2 Maths Quadrilaterals and polygons worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)The diagram shows the letter F. State whether the dashed line is a line of symmetry of the shape.

Answer (a)[1]

(b)The marks on the diagram show what is known about quadrilateral

ABCD

. Write down the most special name of

ABCD

Answer (b)[1]

(c)

ABCD

is a rhombus. Find

x

Answer (c)[2]

(d)The diagram shows a regular pentagon. Find

x

Answer (d)[2]

Answers and worked solutions

Question 1

Answer:

\text{Number of lines of symmetry} = 4

[1]

Lines of symmetry: one along each arm and the two diagonals.

\text{Number of lines of symmetry} = 4

Question 2

Answer:

\text{Order} = 2

[1]

It looks the same every half turn.

\text{Order} = 2

Question 3

Answer:

x = 54

[2]

70^\circ + (2x - 10)^\circ + (2x + 30)^\circ + x^\circ = 360^\circ

(∠ sum of quad.)

5x + 90 = 360

5x = 270

x = 54

Question 4

(a)Answer: TRUE[1]

Every square has diagonals of equal length.True.

(b)Answer: TRUE[1]

Every rhombus has four equal sides.True.

Question 5

Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

Question 6

Answer:

n = 6

[3]

\angle ABC = 180^\circ - 2 \times 30^\circ

\phantom{\angle ABC} = 120^\circ

(∠ sum of △)Exterior angle

= 180^\circ - 120^\circ

= 60^\circ

n = \dfrac{360}{60}

n = 6

Question 7

(a)Answer: NO[1]

Each corner on one side must land exactly on a corner on the other side, and each side on a side.No: the two halves do not match when folded, so the dashed line is not a line of symmetry.

(b)Answer: isosceles trapezium[1]

Equal sides: one pair.Parallel sides: one pair.Right angles: none marked.One pair of parallel sides, the other two sides equal and equal base angles: an isosceles trapezium.

(c)Answer:

x = 28

(∠ sum of △)[2]

\angle BCA = x^\circ

(base ∠s of isos. △)

x^\circ + x^\circ + 124^\circ = 180^\circ

2x = 56

x = 28

(∠ sum of △)

(d)Answer:

x = 108

(∠ sum of polygon)[2]

(5 - 2) \times 180^\circ = 540^\circ

x = \dfrac{540}{5}

x = 108

(∠ sum of polygon)

Question 8

(a)Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

(b)(i)Answer:

n = 18

[2]

8 + 1 = 9

units

\rightarrow 180^\circ

1

unit

\rightarrow \dfrac{180}{9} = 20^\circ

Exterior angle

= 20^\circ

n = \dfrac{360}{20}

n = 18

(b)(ii)Answer: YES[2]

Exterior angle

= 180^\circ - 144^\circ

= 36^\circ

\dfrac{360}{36} = 10

It is a whole number: a regular 10-sided polygon has interior angles of

144^\circ

Question 9

(a)Answer: YES[1]

Each corner on one side must land exactly on a corner on the other side, and each side on a side.Yes: the two halves fold exactly onto each other, so the dashed line is a line of symmetry.

(b)Answer:

\text{Angle} = 180^\circ

°[2]

It looks the same every half turn.

\text{Order} = 2

\text{Angle} = \dfrac{360^\circ}{2}

\text{Angle} = 180^\circ

(c)Answer:

x = 26

°[2]

\angle OBA = 64^\circ

(base ∠s of isos. △)

x = 90 - 64

x = 26

(d)Answer:

x = 52

[2]

(2x - 10)^\circ + (2x + 30)^\circ + x^\circ + 80^\circ = 360^\circ

(∠ sum of quad.)

5x + 100 = 360

5x = 260

x = 52