Choose the correct description of each angle below.
(a)An angle of 24 degrees.(1)
A) acute
B) right angle
C) obtuse
D) straight
E) reflex
(b)An angle of 90 degrees.(1)
A) acute
B) right angle
C) obtuse
D) straight
E) reflex
(c)An angle of 137 degrees.(1)
A) acute
B) right angle
C) obtuse
D) straight
E) reflex
(d)An angle of 180 degrees.(1)
A) acute
B) right angle
C) obtuse
D) straight
E) reflex
(e)An angle of 274 degrees.(1)
A) acute
B) right angle
C) obtuse
D) straight
E) reflex
(Total for Question 1 is 5 marks)
2
Two angles add together to make exactly 180 degrees. What is the name for this pair of angles?
A) complementary
B) supplementary
C) alternate
D) corresponding
E) vertically opposite
(Total for Question 2 is 1 mark)
3
Two angles add together to make exactly 90 degrees. What is the name for this pair of angles?
A) complementary
B) supplementary
C) co-interior
D) reflex
E) equal
(Total for Question 3 is 1 mark)
4
A straight line is divided into two angles by a single ray. One angle is 63 degrees and the other is x degrees. Calculate the value of x.
Diagram NOT accurately drawn
(Total for Question 4 is 2 marks)
5
Three angles meet at a point: 110 degrees, 97 degrees and z degrees. Calculate the value of z.
Diagram NOT accurately drawn
(Total for Question 5 is 2 marks)
6
Two straight lines cross at a point, forming four angles. One of the angles is 105 degrees.
Diagram NOT accurately drawn
(a)State the size of the angle vertically opposite the 105 degree angle.(1)
A) 75
B) 90
C) 105
D) 115
E) 180
(b)Calculate the size of angle x, which is adjacent to the 105 degree angle on the same straight line.(2)
(Total for Question 6 is 3 marks)
7
Triangle DEF is isosceles, with DE = DF. The angle at D (the apex) is 54 degrees. Calculate the size of each base angle, angle DEF and angle DFE.
Diagram NOT accurately drawn
(Total for Question 7 is 3 marks)
8
Quadrilateral WXYZ has angle W = 101 degrees, angle X = 79 degrees, angle Y = 96 degrees and angle Z = x degrees. Calculate the value of x.
Diagram NOT accurately drawn
(Total for Question 8 is 2 marks)
9
Complete each statement about polygons.
(a)A polygon with 3 sides is called a _______.(1)
(b)A polygon with 8 sides is called an _______.(1)
(c)A polygon with 11 sides is called a _______.(1)
(d)A dodecagon has _______ sides.(1)
(e)A quadrilateral has _______ sides.(1)
(Total for Question 9 is 5 marks)
10
Identify the quadrilateral described in each statement.
(a)A quadrilateral with four right angles and four equal sides.(1)
A) square
B) rectangle
C) parallelogram
D) rhombus
E) trapezium
(b)A quadrilateral with four right angles, where opposite sides are equal but not all four sides are equal.(1)
A) square
B) rectangle
C) parallelogram
D) rhombus
E) trapezium
(c)A quadrilateral with two pairs of parallel sides, opposite sides equal but not all four sides equal, and no right angles.(1)
A) square
B) rectangle
C) parallelogram
D) rhombus
E) trapezium
(Total for Question 10 is 3 marks)
11
In triangle LMN, angle L = 63 degrees and angle M = 59 degrees. Side MN is extended to a point O, so that angle LNO is the exterior angle of the triangle at N.
Diagram NOT accurately drawn
(a)Calculate the size of angle LNM, the interior angle at N.(2)
(b)Hence calculate the size of the exterior angle LNO.(2)
(Total for Question 11 is 4 marks)
12
Two parallel lines EF and GH are cut by a transversal. One of the angles formed, at the intersection with EF, is 58 degrees.
Diagram NOT accurately drawn
(a)State the size of the alternate angle to the 58 degree angle at line GH, giving a reason.(1)
(b)Calculate the size of the co-interior (allied) angle to the 58 degree angle at line GH, giving a reason.(2)
(Total for Question 12 is 3 marks)
13
A regular octagon has eight equal sides and eight equal angles.
Diagram NOT accurately drawn
(a)Calculate the size of one exterior angle of the octagon.(2)
(b)Hence calculate the size of one interior angle of the octagon.(2)
(Total for Question 13 is 4 marks)
14
Calculate the sum of the interior angles of a decagon (a 10-sided polygon).
(Total for Question 14 is 2 marks)
15
Identify the type of triangle described by each set of angles.
(a)A triangle with angles 72 degrees, 72 degrees and 36 degrees.(1)
A) equilateral
B) isosceles
C) scalene
D) right-angled
E) obtuse-angled
(b)A triangle with angles 41 degrees, 63 degrees and 76 degrees.(1)
A) equilateral
B) isosceles
C) scalene
D) right-angled
E) obtuse-angled
(c)A triangle with angles 90 degrees, 53 degrees and 37 degrees.(1)
A) equilateral
B) isosceles
C) acute-angled
D) right-angled
E) obtuse-angled
(Total for Question 15 is 3 marks)
16
The bearing of a lighthouse L from a harbour H is 118 degrees. Calculate the bearing of the harbour H from the lighthouse L (the back bearing).
Diagram NOT accurately drawn
A) 062
B) 118
C) 208
D) 242
E) 298
(Total for Question 16 is 1 mark)
17
Complete the table by stating the number of lines of symmetry and the order of rotational symmetry for each shape.
(a)A regular octagon: state the number of lines of symmetry and the order of rotational symmetry.(2)
(b)An isosceles triangle that is not equilateral: state the number of lines of symmetry and the order of rotational symmetry.(2)
(c)A rectangle that is not a square: state the number of lines of symmetry and the order of rotational symmetry.(2)
(Total for Question 17 is 6 marks)
18
Euler's formula for solids states that F + V - E = 2, where F is the number of faces, V is the number of vertices and E is the number of edges.
(a)A square-based pyramid has 5 faces, 5 vertices and 8 edges. Show that this is consistent with Euler's formula.(2)
(b)A different solid has 9 faces and 16 edges. Calculate the number of vertices it must have.(2)
(Total for Question 18 is 4 marks)
19
When a transversal crosses two parallel lines, angles that lie in matching corresponding positions at each intersection are given a special name. What is it?
A) alternate
B) corresponding
C) co-interior
D) vertically opposite
E) supplementary
(Total for Question 19 is 1 mark)
20
When a transversal crosses two parallel lines, angles on opposite sides of the transversal, between the two parallel lines, are given a special name. What is it?
A) alternate
B) corresponding
C) co-interior
D) vertically opposite
E) supplementary
(Total for Question 20 is 1 mark)
21
The three angles of a triangle are x degrees, 3x degrees and 5x degrees. Calculate the value of x and hence find the size of each angle.
Diagram NOT accurately drawn
(Total for Question 21 is 3 marks)
22
Triangle XYZ is isosceles with XY = XZ. Angle X = 68 degrees. Side YZ is extended to a point W. Calculate the size of angle XZW, the exterior angle at Z.
Diagram NOT accurately drawn
(Total for Question 22 is 3 marks)
23
Two squares and a regular pentagon are placed together so that they all meet at a single point, with no overlap. Calculate the size of the gap that remains at that point.
Diagram NOT accurately drawn
(Total for Question 23 is 3 marks)
24
A regular polygon has an interior angle of 140 degrees. Calculate the number of sides the polygon has.
A) 6
B) 8
C) 9
D) 10
E) 12
(Total for Question 24 is 1 mark)
25
A quadrilateral has four angles: 3x degrees, (2x + 10) degrees, (x + 20) degrees and (4x - 10) degrees.
Diagram NOT accurately drawn
(a)Form an equation using the fact that the angles of a quadrilateral sum to 360 degrees, and solve it to find the value of x.(3)
(b)Hence calculate the size of all four angles.(2)
(Total for Question 25 is 5 marks)
Mark scheme · EP.M12B Angles and Shape: Practice Set 2
Question 1
(a) B1 acute cao
(a) Answer: acute
(b) B1 right angle cao
(b) Answer: right angle
(c) B1 obtuse cao
(c) Answer: obtuse
(d) B1 straight (line) cao
(d) Answer: straight
(e) B1 reflex cao
(e) Answer: reflex
Question 2
B1 supplementary cao
Answer: supplementary
Question 3
B1 complementary cao
Answer: complementary
Question 4
M1 180 - 63 seen (angles on a straight line sum to 180 degrees)
A1 117 degrees cao
Answer: x = 117 degrees
Question 5
M1 360 - 110 - 97 seen (angles around a point sum to 360 degrees)
A1 153 degrees cao
Answer: z = 153 degrees
Question 6
(a) B1 105 degrees cao (vertically opposite angles are equal)
(a) Answer: 105 degrees
(b) M1 180 - 105 seen
(b) A1 75 degrees cao
(b) Answer: x = 75 degrees
Question 7
M1 180 - 54 seen
M1 126 / 2 seen (ft)
A1 63 degrees cao (for each base angle)
Answer: angle DEF = angle DFE = 63 degrees
Question 8
M1 360 - 101 - 79 - 96 seen (angles in a quadrilateral sum to 360 degrees)
A1 84 degrees cao
Answer: x = 84 degrees
Question 9
(a) B1 triangle cao
(a) Answer: triangle
(b) B1 octagon cao
(b) Answer: octagon
(c) B1 hendecagon oe (accept undecagon)
(c) Answer: hendecagon
(d) B1 12 cao
(d) Answer: 12
(e) B1 4 cao
(e) Answer: 4
Question 10
(a) B1 square cao
(a) Answer: square
(b) B1 rectangle cao
(b) Answer: rectangle
(c) B1 parallelogram cao
(c) Answer: parallelogram
Question 11
(a) M1 180 - 63 - 59 seen
(a) A1 58 degrees cao
(a) Answer: angle LNM = 58 degrees
(b) M1 180 - their (a) seen, or 63 + 59 (exterior angle = sum of two opposite interior angles)
(b) A1 122 degrees cao (ft)
(b) Answer: angle LNO = 122 degrees
Question 12
(a) B1 58 degrees oe with reason 'alternate angles are equal'
(a) Answer: 58 degrees (alternate angles are equal)
(b) M1 180 - 58 seen
(b) A1 122 degrees cao with reason 'co-interior angles sum to 180 degrees'
(b) Answer: 122 degrees (co-interior angles sum to 180 degrees)
Question 13
(a) M1 360 / 8 seen
(a) A1 45 degrees cao
(a) Answer: 45 degrees
(b) M1 180 - their (a) seen (ft)
(b) A1 135 degrees cao (ft)
(b) Answer: 135 degrees
Question 14
M1 (10 - 2) x 180 seen
A1 1440 degrees cao
Answer: 1440 degrees
Question 15
(a) B1 isosceles cao
(a) Answer: isosceles
(b) B1 scalene cao
(b) Answer: scalene
(c) B1 right-angled cao
(c) Answer: right-angled
Question 16
B1 298 degrees cao (118 + 180)
Answer: 298 degrees
Question 17
(a) B1 8 lines of symmetry cao
(a) B1 order of rotational symmetry 8 cao
(a) Answer: 8 lines of symmetry, order 8 rotational symmetry
(b) B1 1 line of symmetry cao
(b) B1 order of rotational symmetry 1 cao
(b) Answer: 1 line of symmetry, order 1 rotational symmetry
(c) B1 2 lines of symmetry cao
(c) B1 order of rotational symmetry 2 cao
(c) Answer: 2 lines of symmetry, order 2 rotational symmetry
Question 18
(a) M1 5 + 5 - 8 substituted correctly
(a) A1 = 2 cso (matches Euler's formula)
(a) Answer: 2 (consistent with Euler's formula)
(b) M1 9 + V - 16 = 2 seen, rearranged to V = 2 - 9 + 16
(b) A1 9 cao
(b) Answer: 9 vertices
Question 19
B1 corresponding cao
Answer: corresponding
Question 20
B1 alternate cao
Answer: alternate
Question 21
M1 x + 3x + 5x = 180 seen (oe)
A1 x = 20 cao
A1 angles 20 degrees, 60 degrees and 100 degrees all correct (ft)
Answer: x = 20; angles are 20 degrees, 60 degrees and 100 degrees
Question 22
M1 (180 - 68) / 2 seen (base angles of isosceles triangle)
A1 base angle XYZ = XZY = 56 degrees (ft)
A1 180 - 56 = 124 degrees cao (ft), or 68 + 56 = 124
Answer: angle XZW = 124 degrees
Question 23
M1 interior angle of a regular pentagon = 108 degrees found or used
M1 90 + 90 + 108 = 288 seen (oe)
A1 360 - 288 = 72 degrees cao
Answer: 72 degrees
Question 24
B1 9 cao, with working: exterior angle = 180 - 140 = 40, number of sides = 360 / 40 = 9