Shape and Space - part 2
ANGLES AND PARALLEL LINES A
Parallel lines are lines which stay at the same distance apart. They
never meet.
Railway lines are an example

A set of parallel lines is marked with
an arrow to show they are parallel


If there are two different sets of
parallel lines, the second set can be
marked with two arrows.

Interior angles
This line crosses the set of parallel lines.
It is called a transversal.

a
The angles a and b inside the parallel
lines add up to 180°. (You can check it
with a protractor)
b

a + b = 180° (interior angles)
A)
Use this fact to work out angle a in these diagrams, without using
a protractor (give the reason in brackets):
1)
2)

f lex i p

ac k s
3)

40
a

4)

88
a

1
a
152


a
73
Shape and Space - part 2
Try to find angles a, b and c giving the reasons.
* Remember angles on a straight line add up to 180°.
5)
6)

55
a

b
c

7)
148 b
a



a
64
c
c
b
If two lines cross the parallel lines, they will each have their own
completely separate set of angles.
B)
Try these questions:
In the diagrams below, find a, b and c. Then find d, e and f,
treating them as a different question
1)


a c
f
60 b
d
e 80
2)
b
c
93
a


d
f
57
e
f lex i p
Check your answers then discuss with your tutor what you need to
work on next.
ac k s
2
Shape and Space - part 2
Answers
Angles And Parallel Lines A
A)
1)
a = 140° (interior)
2)
a = 92° (interior)
3)
a = 28° (interior)
4)
a = 107° (interior)
5)
a = 125° (interior) b 125° (angles on a straight line)
c = 55°
6)
a = 32° (interior) b 32° (angles on a straight line)
c = 148°
7)
a = 116° (interior) b 116° (angles on a straight line)
c = 64°
B
1)
f lex i p
2)
a = 120°
b = 120°
c = 60°
d = 100°
e = 100°
f = 80°
a = 87°
b = 87°
c = 93°
d = 123°
e = 123°
f = 57°
ac k s
3
Shape and Space - part 2
ANGLES AND PARALLEL LINES B
Alternate angles
You may have noticed in Sheet A that parallel lines make equal angles
too.

60
a
b
Angle a = 120° (interior angle)
So angle b = 60° (straight
line)

This gives us a new angle fact.
Angles in this Z shape are called
alternate angles because they are on
alternate sides of the crossing line.

60
b
Alternate angles are equal

b = 60° (alternate angle)
A)
Try these questions, they are not drawn accurately so don't use a
protractor:
Find angle a
1)
55
a
100
f lex i p
ac k s
2)

46

3)
a

a
4)

80
a

4



Shape and Space - part 2
5)
6)

85
7)

140


a
a
a


Try to mark in the angle which is alternate to a in these questions
8)

a

9)

a

10)

a
f lex i p

ac k s
5
65
Shape and Space - part 2
Corresponding angles

100
a

b
Angle a = 80° (interior angle)
So b = 100° (on a straight line)

This gives another angle fact.
Angles in this F shape are called
corresponding angles because
they are in the same position.
(it is as if the parallel lines were
one line which has split into 2)
100

b
Corresponding angles are equal
b = 100° (corresponding angle)
B)
Try these questions:
Find angle a, and give the reason in brackets.
1)
120
2)


a
3)
49
a

70
6)
85
f lex i p
a
ac k s

a
95
5)

4)

a

80
6
a

Shape and Space - part 2
In these questions, try to mark in the angle which is corresponding to
a.
7)

a

8)

a

9)
a


10)


a
f lex i p
Check your answers then discuss with your tutor what you need to
work on next.
ac k s
7
Shape and Space - part 2
Answers
Angles And Parallel Lines B
A)
1)
a = 55°
2)
a = 46°
3)
a = 100°
4)
a = 80°
5)
a = 85°
6)
a = 140°
7)
a = 65°
B)
a = 120°
(corresponding)
2)
a = 80°
(corresponding)
3)
a = 49°
(corresponding)
4)
a = 70°
(corresponding)
5)
a = 95°
(corresponding)
6)
a = 85°
(corresponding)
f lex i p
1)
ac k s
8
Shape and Space - part 2
ANGLES AND PARALLEL LINES C
This sheet gives practice in finding missing angles. Here is a reminder
of the most important facts so far.
Angle facts:
interior angles add up to 180°
alternate angles are equal
corresponding angles are equal
Other facts:
angles on a straight line = 180°
angles in a triangle = 180°
vertically opposite angles are equal
Try these questions (you won’t need to measure)
Try to find all the missing angles, giving a reason. There is more than
one correct reason for each (though only one correct answer!). It is
usually easier to work through the angles in alphabetical order.
1)

g
f
e
65
d

f lex i p
2)
ac k s
a
c
g

f
95 e

a
d
b c
9
b
Shape and Space - part 2
3)
P
e f
40 g

j
a
d
c
m l
n 30
k
i
b
h

f lex i p
Check your answers then discuss with your tutor what you need to
work on next.
ac k s
10
Shape and Space - part 2
Answers
Angles And Parallel Lines C
1)
2)
f lex i p
3)
a = 115°
b = 65°
c = 115°
e = 115°
f = 65°
g = 115°
a = 85°
b = 95°
c = 85°
e = 85°
f = 95°
g = 85°
a = 40°
b = 140°
c = 40°
d = 140°
e = 140°
f = 40°
g = 140°
h = 30°
I = 150°
j = 30°
k = 150°
l = 150°
m = 30°
n = 150°
p = 110°
ac k s
11
d = 65°
d = 95°