GCSE
Mathematics
Targeting Grade C
Shape and Space
Unit 2 Angles
Can you…
If not you need
• Name angles
TOP Names of angles
• Use angle properties
Practice 1: Simple Angles
• Use triangle angle properties
Try a test
• Understand angles in parallel lines
• Use properties in triangles
Practice 2: Angles in triangles
TAIL 1
Practice 3: parallel lines
Practise 4: Triangles in parallel lines
and parallel lines
Try a test
TAIL 2
TOP Name these angles -
Acute ,
Obtuse ,
a
A
Reflex
B
Name the type of
angle:
Angle BAE
E
Angle DCB
D
C
g
b
Use CAPITAL LETTERS
to denote vertices of a
shape or an angle
d
c
Lesson
Angle EDC
f
e
Remember there can
be more than one angle
at a point
Practice 1: Find the value of the lettered angles and give reasons
1.
2.
45º
122º
yº
yº
81º
xº
3.
68
Lesson
0
37º
Practice 2: Find the value of the lettered angles and give reasons
Diagram NOT
accurately drawn 2.
1.
R
Diagram NOT
accurately drawn
y°
x°
A
y°
48°
B
126° x°
C
P
3.
Q
A
Diagram NOT
accurately drawn
Lesson
62°
x
B
C
D
TAIL 1 - Find the value of the lettered angles and give reasons
1.
x = 360 – (90+60 +100) = 110O
Are you ready for
the answers ?
3.
A
Diagram NOT
accurately drawn
Diagram NOT
accurately drawn
60°
100°
x°
180 – 62 = 118O
62°
x
B
C
X = (180 – 118) /2 = 31O
D
4.
2.
Y = 180 – 72 = 108O
X = 180 – (72 + 72) = 36O
q
q = 102O
p = r = 180 – 102 =
78O
p
102
0
r
Next
Find the value of the lettered angles and give reasons
Are you ready for
the answers ?
5.
y
y = 360 – (35 + 70 + 87)
y = 168
o
Triangles sum to 180
o
Quadrilaterals sum to 360
6.
o
Diagram NOT
accurately drawn
A
100°
D
2x°
3x = 360 – (100 + 47) = 213
o
x = 213/3 = 71
47°
B
x°
C
so 2x = 142
o
o
Lesson
Practice 3: Remember:
Alternate angles are equal and make a Z
•
•
•
•
Corresponding angles are equal and make an F
• •
• •
• •
• •
Allied angles add up to 180 and make a C
•
•
Next
Practice 3: Find the value of the lettered angles and give reasons
1.
A
C
B
38º
ABC is parallel to DEFG.
BE = EF.
Angle ABE = 38°.
Work out x and y, giving reasons
yº
xº
D
E
G
F
2.
Work out x , giving reasons
P
Q
A
C
108º
R
x
S
B
D
Lesson
Practice 4: Find the value of the lettered angles and give reasons
D
3.
72º
C
yº
130º
E
xº
B
Diagram NOT accurately drawn
AC and BD are straight lines which cross at E.
AD is parallel to BC.
Work out x and y, giving reasons
A
4.
Mark with arrows, (>>), a pair of parallel lines.
Mark with the letter R, a right angle.
What type of angle is shown by the letter x?
x
Lesson
Are you ready for
the answers ?
TAIL 2
1.
B
A
C
56º
x
D
F
E
x = 56
o
BEG and CFG are straight lines.
ABC is parallel to DEF.
Angle ABE = 56°
EF = EG
Work out x and y, giving reasons
(alternate angle)
180 – 56 = 124
y = (180 – 124) / 2 = 28
y
(angles on a straight line add up tp 180 and
isosceles triangle has two equal angles
G
2.
Work out x, y, and z giving reasons
100 o
y x
>
x = 100
y = 80
z
o
o
(vertically opposite angles are equal)
o
(angles on a straight line add up to 180 )
>
z = 100
o
(corresponding angles)
Next
Are you ready for
the answers ?
TAIL 2
3.
Work out y, giving reasons
Diagram NOT
accurately drawn
D
62°
E
y°
64°
F
y = 64
o
(alternate angles)
o
Lesson
G