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50 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
Angle rules & giving reasons
13 questions
Lesson
Not started
Mark as done
The diagram shows two straight lines crossing at a point.
126°
x
y
Diagram NOT accurately drawn
(a)
Write down the size of the angle marked
x
x
x
. Give a reason for your answer.
(b)
Work out the size of the angle marked
y
y
y
. Give a reason for your answer.
●●
●●●
Level 2
4 marks
Start
→
Mark as done
The diagram shows three angles on a straight line.
42°
x°
71°
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. Give a reason for your answer.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
The angles of a triangle are
2
x
°
2x°
2
x
°
,
(
3
x
+
10
)
°
(3x + 10)°
(
3
x
+
10
)
°
and
(
x
+
20
)
°
(x + 20)°
(
x
+
20
)
°
.
Work out the size of the largest angle. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A
B
C
ABC
A
B
C
is a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
.
B
C
BC
B
C
is extended to the point
D
D
D
.
Angle
B
A
C
=
44
°
BAC = 44°
B
A
C
=
44°
.
44°
x
A
B
C
D
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
.
Give a reason for each stage of your working. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
A
B
C
ABC
A
B
C
is a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
.
B
C
D
BCD
B
C
D
is a straight line.
Angle
B
A
C
=
44
°
BAC = 44°
B
A
C
=
44°
.
44°
x
A
B
C
D
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The diagram shows a triangle.
(2x + 10)°
(3x − 20)°
(x + 40)°
Diagram NOT accurately drawn
Work out the size of the largest angle of the triangle.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows four angles meeting at a point.
114°
2x°
x°
Diagram NOT accurately drawn
Work out the size of the angle marked
2
x
°
2x°
2
x
°
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Triangle
P
Q
R
PQR
P
QR
has
P
Q
=
P
R
PQ = PR
P
Q
=
P
R
.
Angle
P
Q
R
=
65
°
PQR = 65°
P
QR
=
65°
.
65°
P
Q
R
Diagram NOT accurately drawn
Work out the size of angle
Q
P
R
QPR
QP
R
. Give a reason for each stage of your working.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows two straight lines crossing at a point.
(3x + 10)°
76°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give a reason for your answer.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A
F
B
AFB
A
F
B
and
C
H
G
D
CHGD
C
H
G
D
are parallel lines.
E
F
G
EFG
E
F
G
and
F
H
FH
F
H
are straight lines.
104°
52°
A
B
C
D
E
F
G
H
Show that triangle
F
G
H
FGH
F
G
H
is isosceles.
Give a reason for each stage of your working.
(5 marks)
●●●
●●
Level 3
5 marks
Start
→
Mark as done
The diagram shows a quadrilateral.
(2x − 10)°
(4x + 15)°
(x + 50)°
(3x + 5)°
Diagram NOT accurately drawn
(a)
Work out the size of the smallest angle of the quadrilateral.
(b)
Explain how you can check that your four angles are correct.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The diagram shows a quadrilateral.
x°
85°
95°
2x°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give a reason for your answer.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A
B
C
ABC
A
B
C
is a triangle with
A
B
=
A
C
AB = AC
A
B
=
A
C
.
B
C
D
BCD
B
C
D
is a straight line.
Angle
A
C
D
=
116
°
ACD = 116°
A
C
D
=
116°
.
116°
A
B
C
D
Diagram NOT accurately drawn
Work out the size of angle
B
A
C
BAC
B
A
C
. Give a reason for each stage of your working.
●●●●●
Level 5
4 marks
Start
→
Angles in parallel lines
17 questions
Lesson
Not started
Mark as done
The diagram shows two parallel lines crossed by a straight line.
42°
x
Diagram NOT accurately drawn
(a)
Write down the size of angle
x
x
x
.
(b)
Give a reason for your answer.
●
●●●●
Level 1
2 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
57°
y
Diagram NOT accurately drawn
(a)
Write down the size of the angle marked
y
y
y
.
(b)
Give a reason for your answer.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
64°
x°
Diagram NOT accurately drawn
Write down the size of the angle marked
x
x
x
. Give a reason for your answer.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
138°
y
Diagram NOT accurately drawn
Work out the size of angle
y
y
y
. Give a reason for each step.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
A
B
AB
A
B
and
C
D
CD
C
D
are parallel straight lines.
E
F
EF
E
F
is a straight line.
131°
x
A
B
C
D
E
F
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
.
Give a reason for each stage of your working. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
118°
y°
z°
Diagram NOT accurately drawn
(a)
Work out the size of the angle marked
y
y
y
. Give a reason for your answer.
(b)
Write down the size of the angle marked
z
z
z
. Give a reason for your answer.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
71°
y°
z°
Diagram NOT accurately drawn
(a)
Write down the size of the angle marked
y
y
y
. Give a reason for your answer.
(b)
Work out the size of the angle marked
z
z
z
. Give a reason for your answer.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows two parallel lines and a straight line crossing them.
(2x + 30)°
(3x − 10)°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. (3 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A
F
B
AFB
A
F
B
and
C
H
G
D
CHGD
C
H
G
D
are parallel lines.
E
F
G
EFG
E
F
G
and
F
H
FH
F
H
are straight lines.
104°
52°
A
B
C
D
E
F
G
H
Show that triangle
F
G
H
FGH
F
G
H
is isosceles.
Give a reason for each stage of your working.
(5 marks)
●●●
●●
Level 3
5 marks
Start
→
Mark as done
P
Q
R
S
PQRS
P
QR
S
is a quadrilateral.
4x − 5
3x + 10
5x − 20
3x
P
Q
R
S
The angles are measured in degrees.
Show that
P
Q
R
S
PQRS
P
QR
S
is a trapezium.
(4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
P
Q
PQ
P
Q
and
R
S
RS
R
S
are parallel straight lines.
A
A
A
is a point on
P
Q
PQ
P
Q
, and
B
B
B
and
C
C
C
are points on
R
S
RS
R
S
with
A
B
=
A
C
AB = AC
A
B
=
A
C
.
Angle
P
A
B
=
48
°
PAB = 48°
P
A
B
=
48°
.
48°
P
Q
R
S
A
B
C
Diagram NOT accurately drawn
Work out the size of angle
B
A
C
BAC
B
A
C
. You must give reasons for each stage of your working.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
(3x + 20)°
(2x − 15)°
Diagram NOT accurately drawn
(a)
Work out the value of
x
x
x
.
(b)
Work out the size of the smaller of the two marked angles.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The diagram shows two parallel lines crossed by a straight line.
70°
(2x + 30)°
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Give a reason for your answer.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
A
P
B
APB
A
P
B
and
Q
R
QR
QR
are parallel straight lines.
P
P
P
is joined to
Q
Q
Q
and to
R
R
R
.
Angle
P
Q
R
=
68
°
PQR = 68°
P
QR
=
68°
. Angle
Q
P
R
=
47
°
QPR = 47°
QP
R
=
47°
.
68°
47°
A
P
B
Q
R
Diagram NOT accurately drawn
Work out the size of angle
R
P
B
RPB
R
P
B
. Give a reason for each stage of your working.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
P
Q
R
PQR
P
QR
is a triangle.
P
Q
R
S
T
P
S
Q
PSQ
P
S
Q
and
P
T
R
PTR
P
T
R
are straight lines.
S
T
ST
S
T
is parallel to
Q
R
QR
QR
.
(a)
Prove that triangle
P
Q
R
PQR
P
QR
is similar to triangle
P
S
T
PST
P
S
T
.
(2 marks)
S
T
=
12
ST = 12
S
T
=
12
cm \qquad
Q
R
=
20
QR = 20
QR
=
20
cm \qquad
P
R
=
35
PR = 35
P
R
=
35
cm
(b)
Work out the length of
T
R
TR
T
R
.
(3 marks)
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The diagram shows two parallel lines.
X
X
X
lies on the upper line,
Z
Z
Z
lies on the lower line, and
M
M
M
is a point between the lines.
34°
51°
x°
X
M
Z
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows two parallel lines.
X
X
X
lies on the upper line,
Z
Z
Z
lies on the lower line, and
M
M
M
is a point between the lines.
Angle
X
M
Z
=
81
°
XMZ = 81°
X
M
Z
=
81°
.
(2x)°
81°
(3x + 6)°
X
M
Z
Diagram NOT accurately drawn
Work out the value of
x
x
x
. Show your working clearly, giving reasons.
●●●●●
Level 5
4 marks
Start
→
Interior & exterior angles of polygons
22 questions
Lesson
Not started
Mark as done
Work out the sum of the interior angles of a pentagon.
●
●●●●
Level 1
2 marks
Start
→
Mark as done
The size of each interior angle of a regular hexagon is
Circle your answer.
A
60
°
60°
60°
B
90
°
90°
90°
C
120
°
120°
120°
D
135
°
135°
135°
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Work out the size of each interior angle of a regular polygon with 9 sides.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
A regular polygon has 10 sides.
(a)
Work out the size of each exterior angle.
(b)
Work out the size of each interior angle.
●●
●●●
Level 2
2 marks
Start
→
Mark as done
The interior angles of a pentagon are
100
°
100°
100°
,
110
°
110°
110°
,
120
°
120°
120°
,
x
°
x°
x
°
and
(
x
+
10
)
°
(x + 10)°
(
x
+
10
)
°
.
Work out the value of
x
x
x
. (3 marks)
●●
●●●
Level 2
3 marks
Start
→
Mark as done
The exterior angle of a regular polygon is
24
°
24°
24°
.
(a)
Work out the number of sides of the polygon. [2]
(b)
Work out the size of each interior angle. [1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Five of the interior angles of a hexagon are
130
°
130°
130°
,
120
°
120°
120°
,
110
°
110°
110°
,
140
°
140°
140°
and
100
°
100°
100°
.
Work out the size of the sixth interior angle. [3]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Each interior angle of a regular polygon is
162
°
162°
162°
.
Work out the number of sides of the polygon.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
The diagram shows a pentagon.
97°
134°
83°
x°
112°
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Each exterior angle of a regular polygon is
24
°
24°
24°
.
Work out the number of sides of the polygon.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
(a)
The size of each interior angle of a regular polygon is
156
°
156°
156°
Work out the number of sides of the polygon. (3 marks)
(b)
A different regular polygon has
12
12
12
sides.
Work out the size of each interior angle of this polygon. (1 mark)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
P
Q
R
S
PQRS
P
QR
S
is a quadrilateral.
4x − 5
3x + 10
5x − 20
3x
P
Q
R
S
The angles are measured in degrees.
Show that
P
Q
R
S
PQRS
P
QR
S
is a trapezium.
(4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
P
Q
PQ
P
Q
,
Q
R
QR
QR
,
R
S
RS
R
S
and
S
T
ST
S
T
are four sides of a regular polygon with
n
n
n
sides.
P
Q
R
S
T
U
V
W
Q
R
U
V
W
QRUVW
QR
U
V
W
is a regular pentagon.
R
S
U
RSU
R
S
U
is an equilateral triangle.
Work out the value of
n
n
n
.
You must show all your working.
(4 marks)
●●●
●●
Level 3
4 marks
Start
→
Mark as done
The diagram shows a regular pentagon and a regular hexagon which have a common edge.
a°
Diagram NOT accurately drawn
Work out the size of the angle marked
a
a
a
.
●●●●
●
Level 4
4 marks
Start
→
Mark as done
Each interior angle of a regular polygon
P
P
P
is 4 times the size of each exterior angle.
(a)
Work out the number of sides of polygon
P
P
P
.
Each interior angle of a regular polygon
Q
Q
Q
is
6
°
6°
6°
bigger than each interior angle of polygon
P
P
P
.
(b)
Work out the number of sides of polygon
Q
Q
Q
.
●●●●
●
Level 4
5 marks
Start
→
Mark as done
Five of the interior angles of a hexagon are
130
°
130°
130°
,
145
°
145°
145°
,
105
°
105°
105°
,
118
°
118°
118°
and
132
°
132°
132°
.
Work out the size of the sixth interior angle.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
The sum of the interior angles of a polygon is
1440
°
1440°
1440°
.
(a)
Work out the number of sides of the polygon.
The polygon is regular.
(b)
Work out the size of each exterior angle.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Here is a pentagon.
104°
127°
141°
P
Q
R
S
T
Angle
P
T
S
=
3
×
PTS = 3 \times
P
T
S
=
3
×
angle
P
Q
R
PQR
P
QR
Work out the size of angle
P
T
S
PTS
P
T
S
.
You must show all your working.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
P
P
P
is a regular polygon with 10 sides.
The interior angle of a regular polygon
Q
Q
Q
is
12
°
12°
12°
greater than the interior angle of
P
P
P
.
Work out the number of sides of
Q
Q
Q
.
●●●●●
Level 5
4 marks
Start
→
Mark as done
The diagram shows a regular pentagon
A
B
C
D
E
ABCDE
A
B
C
D
E
. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
cross at the point
F
F
F
.
x°
A
B
C
D
E
F
Diagram NOT accurately drawn
Work out the size of the angle marked
x
x
x
. You must give reasons for each stage of your working.
●●●●●
Level 5
4 marks
Start
→
Mark as done
Ten identical regular octagons are joined together as shown in the diagram.
a
S
The octagons enclose the shape
S
S
S
.
Each side of each octagon has length
a
a
a
.
Find an expression, in terms of
a
a
a
, for the area of
S
S
S
.
Give your answer in the form
p
(
5
+
2
2
)
a
2
p(5 + 2\sqrt{2})a^2
p
(
5
+
2
2
)
a
2
where
p
p
p
is an integer.
You must show all your working.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
The diagram shows a circle, centre
O
O
O
, radius
r
r
r
cm, and two regular octagons.
r cm
O
The sides of the larger octagon are tangents to the circle.
The vertices of the smaller octagon lie on the circle.
By considering perimeters, show that
4
2
−
2
<
π
<
8
(
2
−
1
)
4\sqrt{2 - \sqrt{2}} < \pi < 8(\sqrt{2} - 1)
4
2
−
2
<
π
<
8
(
2
−
1
)
(4 marks)
●●●●●
Level 5
4 marks
Start
→