Foundation Unit 6: Angles
Numerical fluency
1 Work out
a 90 − 25
b 180 – 90
c 180 − 125
d 180 − 75 – 10
e 85 + 145 + 105
f 360 − 90
g 360 − 205
h 360 − 150 − 90 − 20
i 360 − 110 − 85 − 85
Use a number
line.
2 Find the missing numbers.
a 40 +
c 280 +
= 180
= 360
b 180 = 65 +
Use the inverse
operation.
d 360 = 175 +
3 Work out
1
(180 − 66)
2
a (180 − 42) ÷ 2
b 180 − (34 × 2)
c
d 180 − 75 − 10
e 85 + 145 + 105
f 360 − 270
Algebraic fluency
Collect together the terms in x.
Collect together the number terms
4 For each expression
i simplify the expression
Work out the
expression in
brackets first.
ii find its value when x = 50.
a x + 180 + 2x
b 360 – 3x − 90+ x
5 Solve
a 4x = 180
Rearrange to a term in x on the
LHS and a number on the RHS.
b 2x − 75 = 105 − x
Geometrical fluency
6 STEM This is a Bailey truss. It was invented in the Second World War to build bridges.
Perpendicular lines are at at right
angles (90°) to each other.
Parallel lines are always the
same distance apart and never
meet.
a Write a line that is parallel to AB. LM
The line needs to be horizontal, like AB.
Use two letters to describe your choice.
b Write a line that is parallel to HB.
c Write a line that is perpendicular to EF.
d Are LH and JG perpendicular? Explain your answer.
The line needs to be horizontal, at 90° to EF.
7 For each angle write if it is acute, obtuse or reflex.
..............
................
..................
An acute angle is smaller
than 90°.
An obtuse angle is
between 90° and 180°.
A reflex angle is between
180° and 360°.
8 Is each angle acute, obtuse or reflex?
a 224°
b 167°
c 356°
d 79°
e 95°
f 123°
9 i Estimate the size of each angle.
ii Check your answers by measuring.
i
i
i
ii
ii
ii
10 Work out the size of the unknown angles.
m = 180° – 130°
=
n=
The angles on a straight
line add up to 180°.
a + b = 180
=
11 Work out the size of the angles marked with letters.
Literacy hint
When two straight
lines cross, two pairs
of vertically opposite
angles are created.
Vertically opposite
angles are equal.
12 Write down the name of each of these angles.
The diagram shows
XYZ. The angle is always at
the middle letter. It can also be
written as
XŶZ .
13 For each triangle write down if it is scalene,
isosceles or equilateral.
How many
angles are
equal?
‘Same arcs’
means ‘same
angles’.
 The number of equal sides and angles
can help you identify a triangle.
 Equal sides are marked using a dash.
 Equal angles are shown using the same
number of arcs.
14
a For each triangle, write down if it is scalene, isosceles or equilateral.
A shape has line
symmetry if one half folds
exactly on top of the other
half.
The dashed line is called
a line of symmetry.
b Draw any lines of symmetry on each triangle.
The properties of a shape are facts about its sides, angles, diagonals and symmetry.
Here are some of the properties of some well-known quadrilaterals.
Square




all sides are equal in length
opposite sides are parallel
all angles are 90º
diagonals bisect each other at 90º
Rectangle




opposite sides are equal in length
opposite sides are parallel
all angles are 90º
diagonals bisect each other
Rhombus




all sides are equal in length
opposite sides are parallel
opposite angles are equal
diagonals bisect each other at 90º
Parallelogram




opposite sides are equal in length
opposite sides are parallel
opposite angles are equal
diagonals bisect each other
Trapezium
 1 pair of parallel sides
Isosceles trapezium
 2 sides are equal in length
Kite
 2 pairs of sides are equal in length
 no parallel lines
 1 pair of equal angles
 diagonals bisect each other at 90º
 1 pair of parallel sides
 2 pairs of equal angles
15 a Write down the name of each quadrilateral.
b Draw the lines of symmetry on each shape.
16
A shape has rotational symmetry if
it looks the same more than once in
a full turn.
Find the order of rotational symmetry for each shape.
17 a How many lines of symmetry does a regular pentagon have?
The shape looks the same in three
positions, so it has rotational
symmetry of order 3.
b What is the order of rotational symmetry of a regular pentagon?
a
lines of symmetry
b rotational symmetry of order
How many ways can you
fold a pentagon in half?
Rotate the pentagon a full
turn. In how many positions
does it look the same?
18 a Draw the lines of symmetry on this regular octagon.
b How many lines of symmetry does it have?
c What is the order of rotational symmetry of a regular octagon?
19 Complete the shape.
20 Work out angle a in the quadrilateral.
Angles in a quadrilateral
add up to 360°.
21 Problem-solving Find the coordinates of the fourth vertex of a
a kite with vertices (4, 8), (2, 6), (4, 1)
b rectangle with vertices (–3, 2), (–6, 2), (–6, 7)
Plot the three coordinates on a set of axes.
Join the points.
A kite has two pairs of sides equal in length, so
the fourth vertex must have y-coordinate ☐.
Foundation Unit 6 answers
1 a 65
8 a reflex
b 90
b obtuse
c 55
c reflex
d 95
d acute
e 335
e obtuse
f
270
g 155
f
9 a 95°
h 100
i
b 55°
80
2 a 140
b 115
c 120°
10 a 50°
c 80
b 145°
d 185
c 35°
d 137°
3 a 69
b 112
e 68°
c 57
f
d 95
g 50°
e 335
f
b c = 145°
180 + 3x
ii 330
b i
156°
11 a a = 40°, b = 140°
90
4 a i
270 − 2x
ii 170
c d = 35°
12 a XYZ
b DEF
13 a equilateral
5 a 45 = x
b scalene
b x = 60
6 b LG, LD, GD or JF
c isosceles
14 a i
c e.g. DE, CE, BE, AE, IJ, IK, IL, IM, AB, AC, ...
equilateral
ii isoceles
d No; e.g. they are not at 90°.
iii scalene
7 a reflex
b
b acute
c obtuse
obtuse
15 a i
square
ii rectangle
19
iii parallelogram
iv trapezium
v kite
b
20 130° (angles in a quadrilateral sum to
360°)
21 a (6, 6)
b (−3, 7)
16 a 4
b 6
c 2
d 0
17 a 5 lines
b order 5
18 a
b 8 lines
c order 8