Chapter 14 Practice Paper: Angles, polygons and constructions — question paper (print)

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QQ/GCSE-MATHS/CH14

GCSE (9–1) · GCSE Mathematics (Foundation with Higher stretch)

Chapter 14 Practice Paper

Angles, polygons and constructions

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Answer all questions.
Section A contains ten multiple-choice questions. Choose one answer, A, B, C or D, for each.
Section B contains structured questions. Write your answers in the spaces provided.
Give a reason for each angle you find.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total mark for this paper is 30.

Original practice material written for the MOE GCSE Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 14: angles at a point and on a line, vertically opposite angles, parallel-line rules, triangle and quadrilateral facts, interior and exterior angles of polygons, ruler-and-compass constructions and loci regions.

For Examiner’s Use
Section A	/ 10
Section B	/ 20
Total	/ 30

Section A: Multiple-choice questions[10 marks]

Choose one answer for each question. Every correct answer scores one mark.

1
An angle of 142° sits on a straight line. Its supplement measures
1. A218°
2. B38°
3. C142°
4. D52°
( )
2
Where two straight lines cross, the angle facing a 29° corner measures
1. A151°
2. B58°
3. C29°
4. D90°
( )
3
A right-angled triangle has a second angle of 31°. The third angle is
1. A149°
2. B59°
3. C121°
4. D31°
( )
4
Between two parallel lines, the co-interior partner of a 74° angle is
1. A74°
2. B16°
3. C286°
4. D106°
( )
5
A four-sided field has internal angles of 91°, 84° and 96° at three corners. The fourth corner angle is
1. A89°
2. B99°
3. C271°
4. D90°
( )
6
Adding all six interior angles of a hexagon gives
1. A540°
2. B360°
3. C720°
4. D900°
( )
7
A regular pentagon splits its 540° of interior angles equally. One interior angle is
1. A108°
2. B72°
3. C100°
4. D120°
( )
8
For a regular polygon with 30° exterior angles, the number of sides is
1. A9 sides
2. B15 sides
3. C10 sides
4. D12 sides
( )
9
Every point on the perpendicular bisector of AB is
1. Aequidistant from A and B
2. Btwice as far from A as from B
3. Cexactly 1 cm from AB
4. Don the segment AB only
( )
10
All points exactly 4 cm from the line PQ together form
1. Aa circle of radius 4 cm
2. Bthe perpendicular bisector of PQ
3. Ctwo parallel lines 4 cm either side of PQ
4. Da line 8 cm long
( )

Section B: Structured questions[20 marks]

Show all your working. Marks are given for the reason as well as for the final answer.

11
Solving with angle sums.
1. (a)
  Angles of (4x)° and (2x)° sit together on a straight line. Find x and the larger angle.
  [2]
2. (b)
  Three angles meet at a point: 3x°, 2x° and 90°. Find x.
  [2]
12
Parallel lines.
1. (a)
  A transversal makes 65° with parallel line AB. Write down the corresponding angle on the parallel line CD.
  [1]
2. (b)
  Find the co-interior partner of that 65° angle on CD, with your reason.
  [2]
3. (c)
  Name the rule used in part (a).
  [1]
13
Polygons.
1. (a)
  Find the sum of the interior angles of a 7-sided polygon (heptagon).
  [2]
2. (b)
  A regular polygon has 15 sides. Find each interior angle.
  [2]
14
Triangles.
1. (a)
  In a triangle, two interior angles measure 43° and 66°. Work out the exterior angle at the third vertex.
  [2]
2. (b)
  The apex of an isosceles triangle measures 36°. How big is each base angle?
  [2]
15
A sprinkler between two paths. (Higher)
1. (a)
  Two straight paths meet at 60°. Describe how to construct the set of points equidistant from both paths.
  [2]
2. (b)
  A sprinkler stands on that construction, exactly 2 m from the corner. How far is it from each path?
  [2]

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