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Geometry: Properties of Shapes and Angles (Year 6) - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 5)Geometry: Properties of Shapes and Angles (Year 6) revision guide

This topic is chapter 5 of KS2 Maths: Geometry Practice Book.

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KS2 · Geometry

8.8 Geometry: Properties of Shapes and Angles (Year 6)

Calculators not allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Name the shape that has exactly four equal sides and four right angles.
(1)
2
A quadrilateral has three angles measuring 95 degrees, 80 degrees and 65 degrees. Find the size of the fourth angle.
(2)
3
Explain why the angles on a straight line add up to 180 degrees. Give a short reason.
(2)
4
A regular pentagon has side length 6 cm. Calculate the sum of its interior angles, then give the size of one interior angle.
(2)
5
A student draws a quadrilateral with three right angles. Explain whether the fourth angle must be a right angle. Give a short reason.
(2)
6
In a circle, an arc has a central angle of 140 degrees. What is the size of the reflex angle outside that arc (the larger angle around the circle)?
(2)
7
Triangle ABC is isosceles with AB = AC. The angle at A is 40 degrees. Find the size of each base angle at B and C.
(2)
8
A rectangle has been split into two triangles by a diagonal. One triangle has angles 90 degrees and 30 degrees. Find the three angles of the other triangle formed by the same diagonal.
(2)
9
A student says that a regular polygon with each interior angle 150 degrees must be a regular dodecagon. Is the student correct? Explain your answer and show how you decide which regular polygon it is.
(2)
10
A quadrilateral has sides of equal length and opposite angles equal. Is this enough to say it is a parallelogram, a rhombus, or both? Give the correct name and a short explanation.
(3)
11
One angle in a triangle is 90 degrees and the other two angles are equal. Work out the size of each of the equal angles.
(2)
12
A regular hexagon has interior angles that are all the same. Calculate the size of one interior angle of a regular hexagon.
(2)
13
The angles in a quadrilateral are in the ratio 2:3:4:5. Work out the size of the smallest angle.
(2)
14
A circle is split into three parts. Two central angles are 110 degrees and 85 degrees. What is the size of the third central angle?
(2)
15
A regular hexagon has six equal interior angles. Work out the size of one interior angle.
(2)
16
Draw a shape with exactly one pair of parallel sides and no right angles. Give the name of the shape.
(2)
17
A kite has two equal adjacent sides and one diagonal that bisects the other at right angles. If one angle between the unequal sides is 70 degrees, what is the opposite angle between the unequal sides?
(2)
18
In the diagram a straight line meets two parallel lines. One acute angle is 62 degrees. Work out the corresponding angle on the other parallel line.
(2)
Mark scheme · 8.8 Geometry: Properties of Shapes and Angles (Year 6)

Question 1

  • B1 square cao
  • Answer: square

Question 2

  • M1 Add 95+80+65 = 240 seen
  • B1 360 - 240 = 120 degrees cao
  • Answer: 120 degrees

Question 3

  • M1 Reference to straight line as half turn or sum of two right angles
  • B1 Conclusion that sum is 180 degrees cao
  • Answer: A straight line is a half turn (180 degrees), so angles on it add to 180 degrees

Question 4

  • M1 Use (n-2)x180 = 3x180 = 540 or show sum of interior angles
  • B1 One interior angle = 540/5 = 108 degrees cao
  • Answer: 108 degrees

Question 5

  • M1 State that angles in quadrilateral sum to 360 degrees or show 90+90+90 = 270
  • B1 Fourth angle = 360 - 270 = 90 degrees, so it must be a right angle cao
  • Answer: Yes. The angles sum to 360 so fourth angle = 360 - 270 = 90 degrees

Question 6

  • M1 Recognise reflex angle = 360 - central angle or show 360 - 140
  • B1 Reflex angle = 220 degrees cao
  • Answer: 220 degrees

Question 7

  • M1 Use sum of angles in triangle: 180 - 40 = 140 seen
  • B1 Base angles each 70 degrees cao
  • Answer: 70 degrees

Question 8

  • M1 Recognise triangles share the diagonal and angles at rectangle corners are right angles
  • B1 Other triangle angles are 90 degrees, 60 degrees and 30 degrees cao
  • Answer: 90 degrees, 60 degrees, 30 degrees

Question 9

  • M1 Show relationship interior angle = 180 - (360/n) or compute exterior angle 30 degrees
  • B1 n = 360/30 = 12; student is correct that it is a dodecagon cao
  • Answer: Yes. Exterior angle = 180 - 150 = 30, so n = 360/30 = 12

Question 10

  • M1 State that equal side lengths and opposite equal angles imply opposite sides are parallel or argue properties
  • B1 Name given as rhombus cao
  • B1 Brief reason: all sides equal and opposite angles equal meet rhombus properties (also is a parallelogram) cao
  • Answer: A rhombus. Four equal sides and opposite equal angles fit a rhombus; it is also a parallelogram.

Question 11

  • M1 Subtract 90 from 180 to get 90 or equivalent working
  • B1 Each equal angle 45 degrees cao
  • Answer: 45 degrees

Question 12

  • M1 Use (n-2)x180 = 4x180 = 720 or show sum of interior angles
  • B1 720/6 = 120 degrees cao
  • Answer: 120 degrees

Question 13

  • M1 Sum ratios = 14 and show 360 divided by 14 or equivalent working
  • B1 Smallest angle = 2 x (360/14) = 51 3/7 degrees or 51.428... degrees cao
  • Answer: 51.4285714286 degrees

Question 14

  • M1 Add 110 and 85 to get 195 or equivalent
  • B1 360 - 195 = 165 degrees cao
  • Answer: 165 degrees

Question 15

  • M1 Interior angle sum = (6 - 2) x 180 = 720 degrees, or 360 / 6 = 60 seen
  • B1 720 / 6 = 120 degrees cao
  • Answer: 120 degrees

Question 16

  • M1 A correct trapezium drawn (one pair of parallel sides, no right angles) or equivalent
  • B1 Name given as trapezium cao
  • Answer: trapezium

Question 17

  • M1 Reference to kite symmetry or properties showing opposite angle between unequal sides is equal
  • B1 Answer 70 degrees cao
  • Answer: 70 degrees

Question 18

  • M1 Identify corresponding angles are equal
  • B1 Answer 62 degrees cao
  • Answer: 62 degrees

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